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Lundow, Per-Håkanorcid.org/0000-0002-6291-5885

Open this publication in new window or tab >>On a generalised Lambert *W* branch transition function arising from *p*,*q*-binomial coefficients### Åhag, Per

### Czyż, R.

### Lundow, Per-Håkan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_some",{id:"formSmash:j_idt204:0:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_otherAuthors",{id:"formSmash:j_idt204:0:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_otherAuthors",multiple:true}); 2024 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 462, article id 128347Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2024
##### Keywords

Generalization of Lambert W function, Lenz-Ising model, Magnetization distribution, p, q-binomial coefficients, Special functions
##### National Category

Discrete Mathematics
##### Identifiers

urn:nbn:se:umu:diva-214983 (URN)10.1016/j.amc.2023.128347 (DOI)2-s2.0-85172163818 (Scopus ID)
#####

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Available from: 2023-10-13 Created: 2023-10-13 Last updated: 2023-10-13Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, Kraków, Poland.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

With only a complete solution in dimension one and partially solved in dimension two, the Lenz-Ising model of magnetism is one of the most studied models in theoretical physics. An approach to solving this model in the high-dimensional case (d>4) is by modelling the magnetisation distribution with p,q-binomial coefficients. The connection between the parameters p,q and the distribution peaks is obtained with a transition function ω which generalises the mapping of Lambert W function branches W0 and W−1 to each other. We give explicit formulas for the branches for special cases. Furthermore, we find derivatives, integrals, parametrizations, series expansions, and asymptotic behaviours.

Open this publication in new window or tab >>Revising the universality class of the four-dimensional Ising model### Lundow, Per-Håkan

### Markström, Klas

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_some",{id:"formSmash:j_idt204:1:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_otherAuthors",{id:"formSmash:j_idt204:1:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 993, article id 116256Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Other Physics Topics
##### Identifiers

urn:nbn:se:umu:diva-212073 (URN)10.1016/j.nuclphysb.2023.116256 (DOI)2-s2.0-85163809991 (Scopus ID)
#####

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Available from: 2023-07-18 Created: 2023-07-18 Last updated: 2023-07-18Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

The aim of this paper is to determine the behavior of the specific heat of the 4-dimensional Ising model in a region around the critical temperature, and via that determine if the Ising model and the ϕ4-model belong to the same universality class in dimension 4. In order to do this we have carried out what is currently the largest scale simulations of the 4-dimensional Ising model, extending the lattices size up to L=256 and the number of samples per size by several orders of magnitude compared to earlier works, keeping track of data for both the canonical and microcanonical ensembles. Our conclusion is that the Ising model has a bounded specific heat, while the ϕ4-model is known to have a logarithmic divergence at the critical point. Hence the two models belong to distinct universality classes in dimension 4.

Open this publication in new window or tab >>Damage spreading in the random cluster model### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_some",{id:"formSmash:j_idt204:2:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_otherAuthors",{id:"formSmash:j_idt204:2:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_otherAuthors",multiple:true}); 2022 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 985, article id 116008Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2022
##### National Category

Probability Theory and Statistics
##### Identifiers

urn:nbn:se:umu:diva-201197 (URN)10.1016/j.nuclphysb.2022.116008 (DOI)000882463500012 ()2-s2.0-85141244404 (Scopus ID)
#####

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Available from: 2022-12-01 Created: 2022-12-01 Last updated: 2023-03-24Bibliographically approved

We investigate the damage spreading effect in the Fortuin-Kasteleyn random cluster model for 2- and 3-dimensional grids with periodic boundary. For 2D the damage function has a global maximum at p=q/(1+q) for all q>0 and also local maxima at p=1/2 and p=q/(1+q) for q≲0.75. For 3D we observe a local maximum at p=q/(1+q) for q≲0.46 and a global maximum at p=1/2 for q≲4.5. The chaotic phase of the model's (p,q)-parameter space is where the coupling time is of exponential order and we locate points on its boundary. For 3-dimensional grids the lower bound of this phase may be equal to the corresponding critical point of the q-state Potts model for q≥3.

Open this publication in new window or tab >>Efficient computation of permanents, with applications to Boson sampling and random matrices### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Markström, Klas

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_some",{id:"formSmash:j_idt204:3:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_otherAuthors",{id:"formSmash:j_idt204:3:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_otherAuthors",multiple:true}); 2022 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 455, article id 110990Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Academia Press, 2022
##### Keywords

Boson sampling, Linear optics, Permanent
##### National Category

Computer Sciences Probability Theory and Statistics
##### Identifiers

urn:nbn:se:umu:diva-192500 (URN)10.1016/j.jcp.2022.110990 (DOI)000762463300004 ()2-s2.0-85124124557 (Scopus ID)
#####

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##### Funder

Swedish Research Council, 2014-4897Swedish National Infrastructure for Computing (SNIC)
Available from: 2022-02-24 Created: 2022-02-24 Last updated: 2023-09-05Bibliographically approved

In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we first discuss how to compute the permanent efficiently on a parallel computer, followed by algorithms which provide an exponential speed-up for sparse matrices and linear run times for matrices of limited bandwidth. The parallel algorithm has been implemented in a freely available software package, also available in an efficient serial version. As part of the timing runs for this package we set a new world record for the matrix order on which a permanent has been computed. Next we perform a simulation study of several conjectures regarding the distribution of the permanent for random matrices. Here we focus on permanent anti-concentration conjecture, which has been used to find the classical computational complexity of Boson sampling. We find a good agreement with the basic versions of these conjectures, and based on our data we propose refined versions of some of them. For small systems we also find noticeable deviations from a proposed strengthening of a bound for the number of photons in a Boson sampling system.

Open this publication in new window or tab >>Boundary effects on finite-size scaling for the 5-dimensional Ising model### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_some",{id:"formSmash:j_idt204:4:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_otherAuthors",{id:"formSmash:j_idt204:4:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_otherAuthors",multiple:true}); 2021 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 967, article id 115422Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2021
##### National Category

Other Physics Topics
##### Identifiers

urn:nbn:se:umu:diva-183135 (URN)10.1016/j.nuclphysb.2021.115422 (DOI)000655593800022 ()2-s2.0-85104919359 (Scopus ID)
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Available from: 2021-05-17 Created: 2021-05-17 Last updated: 2023-09-05Bibliographically approved

High-dimensional (d≥5) Ising systems have mean-field critical exponents. However, at the critical temperature the finite-size scaling of the susceptibility χ depends on the boundary conditions. A system with periodic boundary conditions then has χ ∝ L^{5/2}. Deleting the 5L^{4} boundary edges we receive a system with free boundary conditions and now χ ∝ L^{2}. In the present work we find that deleting the L^{4 }boundary edges along just one direction is enough to have the scaling χ ∝ L2. It also appears that deleting L^{3} boundary edges results in an intermediate scaling, here estimated to χ ∝ L^{2.275}. We also study how the energy and magnetisation distributions change when deleting boundary edges.

Open this publication in new window or tab >>Are we ready for agenda 2030 for Sustainable Development?### Åhag, Per

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Hed, Lisa

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Olsson, Leif

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_some",{id:"formSmash:j_idt204:5:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_otherAuthors",{id:"formSmash:j_idt204:5:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_otherAuthors",multiple:true}); 2019 (English)In: 2019 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), IEEE, 2019, p. 224-227Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

IEEE, 2019
##### Series

IEEE International Conference on Industrial Engineering and Engineering Management, E-ISSN 2157-362X
##### Keywords

Agenda 2030, Education for sustainable development, higher education, Industrial Engineering and Management
##### National Category

Pedagogy
##### Research subject

sustainable development
##### Identifiers

urn:nbn:se:umu:diva-186169 (URN)10.1109/IEEM44572.2019.8978861 (DOI)2-s2.0-85079643165 (Scopus ID)978-1-7281-3805-3 (ISBN)978-1-7281-3804-6 (ISBN)
##### Conference

2019 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), IEEE, 2019, Macau, China, December 15-18, 2019
#####

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Available from: 2021-07-15 Created: 2021-07-15 Last updated: 2023-03-24Bibliographically approved

Department of Information Systems and Technology, Mid Sweden University, Sundsvall, Sweden.

Are we as educators of future engineers ready for the United Nations Agenda 2030 for sustainable development? We make a comparative study of the Master's programme in Industrial Engineering and Management at two Swedish Universities. Our conclusion is that we as educators and programme managers are not yet in the right process for Agenda 2030 and the necessary transition into a sustainable future.

Open this publication in new window or tab >>Hyperscaling Violation in Ising Spin Glasses### Campbell, Ian A.

### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_some",{id:"formSmash:j_idt204:6:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_otherAuthors",{id:"formSmash:j_idt204:6:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_otherAuthors",multiple:true}); 2019 (English)In: Entropy, E-ISSN 1099-4300, Vol. 21, no 10, article id 978Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

MDPI, 2019
##### Keywords

spin glasses, random interactions, scaling, hyperscaling
##### National Category

Probability Theory and Statistics
##### Identifiers

urn:nbn:se:umu:diva-165329 (URN)10.3390/e21100978 (DOI)000495094000060 ()2-s2.0-85074015170 (Scopus ID)
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Available from: 2019-12-02 Created: 2019-12-02 Last updated: 2023-03-28Bibliographically approved

In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above the upper critical dimension. It was shown by M. Schwartz in 1991 that hyperscaling can also break down in Ising systems with quenched random interactions; Random Field Ising models, which are in this class, have been intensively studied. Here, numerical Ising Spin Glass data relating the scaling of the normalized Binder cumulant to that of the reduced correlation length are presented for dimensions 3, 4, 5, and 7. Hyperscaling is clearly violated in dimensions 3 and 4, as well as above the upper critical dimension D=6. Estimates are obtained for the "violation of hyperscaling exponent" values in the various models.

Open this publication in new window or tab >>Revisiting the cavity-method threshold for random 3-SAT### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Markström, Klas

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_some",{id:"formSmash:j_idt204:7:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_otherAuthors",{id:"formSmash:j_idt204:7:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_otherAuthors",multiple:true}); 2019 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 99, no 2, article id 022106Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

American Physical Society, 2019
##### National Category

Probability Theory and Statistics
##### Identifiers

urn:nbn:se:umu:diva-162509 (URN)10.1103/PhysRevE.99.022106 (DOI)000458140700001 ()30934345 (PubMedID)2-s2.0-85061557736 (Scopus ID)
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Available from: 2019-08-21 Created: 2019-08-21 Last updated: 2023-03-23Bibliographically approved

A detailed Monte Carlo study of the satisfiability threshold for random 3-SAT has been undertaken. In combination with a monotonicity assumption we find that the threshold for random 3-SAT satisfies α_{3}≤4.262. If the assumption is correct, this means that the actual threshold value for *k*=3 is lower than that given by the cavity method. In contrast the latter has recently been shown to give the correct value for large *k*. Our result thus indicate that there are distinct behaviors for *k* above and below some critical *k _{c}*, and the cavity method may provide a correct mean-field picture for the range above

Open this publication in new window or tab >>A counterexample to a conjecture by Blocki-Zwonek### Åhag, Per

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Czyz, Rafal

### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_some",{id:"formSmash:j_idt204:8:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_otherAuthors",{id:"formSmash:j_idt204:8:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_otherAuthors",multiple:true}); 2018 (English)In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 27, no 1, p. 119-124Article in journal (Refereed) Published
##### Place, publisher, year, edition, pages

Philadelphia: Taylor & Francis, 2018
##### Keywords

Błocki–Zwonek conjectures, Bergman kernel, Green functions, Jacobi functions
##### National Category

Mathematical Analysis Computational Mathematics
##### Identifiers

urn:nbn:se:umu:diva-125362 (URN)10.1080/10586458.2016.1230913 (DOI)000435506900011 ()2-s2.0-84991029162 (Scopus ID)
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Available from: 2016-09-09 Created: 2016-09-09 Last updated: 2023-09-05Bibliographically approved

Open this publication in new window or tab >>Bimodal Ising spin glass in two dimensions: the anomalous dimension η### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Campbell, I. A.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_some",{id:"formSmash:j_idt204:9:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_otherAuthors",{id:"formSmash:j_idt204:9:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_otherAuthors",multiple:true}); 2018 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 97, no 2, article id 024203Article in journal (Refereed) Published
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American Physical Society, 2018
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Other Physics Topics
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urn:nbn:se:umu:diva-144836 (URN)10.1103/PhysRevB.97.024203 (DOI)000423340800006 ()2-s2.0-85040920775 (Scopus ID)
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Available from: 2018-02-28 Created: 2018-02-28 Last updated: 2023-03-24Bibliographically approved

Direct measurements of the spin glass correlation function G(R) for Gaussian and bimodal Ising spin glasses in dimension two have been carried out in the temperature region T ∼ 1. In the Gaussian case the data are consistent with the known anomalous dimension value η ≡ 0. For the bimodal spin glass in this temperature region T > T*(L), well above the crossover T*(L) to the ground-state-dominated regime, the effective exponent η is clearly nonzero and the data are consistent with the estimate η ∼ 0.28(4) given by McMillan in 1983 from similar measurements. Measurements of the temperature dependence of the Binder cumulant U_{4}(T, L) and the normalized correlation length ξ(T, L)/L for the two models confirms the conclusion that the two-dimensional (2D) bimodal model has a nonzero effective η both below and above T*(L). The 2D bimodal and Gaussian interaction distribution Ising spin glasses are not in the same universality class.