Finite size scaling in the dimer and six-vertex model

Standard

Finite size scaling in the dimer and six-vertex model. / Belov, P. A.; Enin, A. I.; Nazarov, A. A.

In: Journal of Physics: Conference Series, Vol. 1135, No. 1, 012024, 20.12.2018.

Research output: Contribution to journal › Conference article › peer-review

Author

Belov, P. A. ; Enin, A. I. ; Nazarov, A. A. / Finite size scaling in the dimer and six-vertex model. In: Journal of Physics: Conference Series. 2018 ; Vol. 1135, No. 1.

BibTeX

@article{fdc887a47ad1408593c19d67255ff51c,

title = "Finite size scaling in the dimer and six-vertex model",

abstract = "We present results of the Monte-Carlo simulations for scaling of the free energy in dimers on the hexagonal lattice. The traditional Markov-chain Metropolis algorithm and more novel non-Markov Wang-Landau algorithm are applied. We compare the calculated results with the theoretical prediction for the equilateral hexagon and show that the latter algorithm gives more precise results for the dimer model. For a non-hexagonal domain the theoretical results are not available, so we present the numerical results for a certain geometry of the domain. We also study the two-point correlation function in simulations of dimers and the six-vertex model. The logarithmic dependence of the correlation function on the distance, which is in accordance with the Gaussian free field description of fluctuations, is obtained.",

author = "Belov, {P. A.} and Enin, {A. I.} and Nazarov, {A. A.}",

year = "2018",

month = dec,

day = "20",

doi = "10.1088/1742-6596/1135/1/012024",

language = "English",

volume = "1135",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing Ltd.",

number = "1",

note = "International Conference PhysicA.SPb 2018 ; Conference date: 23-10-2018 Through 25-10-2018",

}

RIS

TY - JOUR

T1 - Finite size scaling in the dimer and six-vertex model

AU - Belov, P. A.

AU - Enin, A. I.

AU - Nazarov, A. A.

PY - 2018/12/20

Y1 - 2018/12/20

N2 - We present results of the Monte-Carlo simulations for scaling of the free energy in dimers on the hexagonal lattice. The traditional Markov-chain Metropolis algorithm and more novel non-Markov Wang-Landau algorithm are applied. We compare the calculated results with the theoretical prediction for the equilateral hexagon and show that the latter algorithm gives more precise results for the dimer model. For a non-hexagonal domain the theoretical results are not available, so we present the numerical results for a certain geometry of the domain. We also study the two-point correlation function in simulations of dimers and the six-vertex model. The logarithmic dependence of the correlation function on the distance, which is in accordance with the Gaussian free field description of fluctuations, is obtained.

AB - We present results of the Monte-Carlo simulations for scaling of the free energy in dimers on the hexagonal lattice. The traditional Markov-chain Metropolis algorithm and more novel non-Markov Wang-Landau algorithm are applied. We compare the calculated results with the theoretical prediction for the equilateral hexagon and show that the latter algorithm gives more precise results for the dimer model. For a non-hexagonal domain the theoretical results are not available, so we present the numerical results for a certain geometry of the domain. We also study the two-point correlation function in simulations of dimers and the six-vertex model. The logarithmic dependence of the correlation function on the distance, which is in accordance with the Gaussian free field description of fluctuations, is obtained.

UR - http://www.scopus.com/inward/record.url?scp=85059391353&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1135/1/012024

DO - 10.1088/1742-6596/1135/1/012024

M3 - Conference article

AN - SCOPUS:85059391353

VL - 1135

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012024

T2 - International Conference PhysicA.SPb 2018

Y2 - 23 October 2018 through 25 October 2018

ER -

ID: 38813676