Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Physical Society of Japan

Finite Size Effect in the Quasi-One-Dimensional Ising Model

Kyu Won Lee

Published Nov 15, 2002• 2 citations
Publisher

Abstract

We have studied the finite size effect in the quasi-one-dimensional Ising model by using a Monte Carlo simulation. A marked finite size effect was found with decreasing interchain interaction. Aside from the well-known dimensional crossover from 3D to 1D, a dimensional crossover from 3D to 2D at a crossover size L c (λ) ∼-1/(λln λ) was revealed as an origin of the finite size effect, where λ is the ratio of the interchain interaction to the intrachain one.

DOI
10.1143/jpsj.71.2591

Related papers

Size-driven dimensional crossover in the quasi-one-dimensional Heisenberg model

Kyu Won Lee, Cheol Eui Lee

The finite-size effect in the quasi-one-dimensional (quasi-1D) Heisenberg model was studied by using a Monte Carlo simulation. As a result, a marked finite-size effect was found with decreasing interchain interaction. Aside from the well-known three- to one-dimensional crossover, a size-driven three- to two-dimensional crossover at a crossover anisotropy, depending on the interchain to intrachain interaction ratio and the system size, was revealed to be the origin of the finite-size effect.

Physical Review B•Mar 24, 2004•3 citations

Shape effects of finite-size scaling functions for anisotropic three-dimensional Ising models

Kazuhisa Kaneda, Yutaka Okabe, Macoto Kikuchi

The finite-size scaling (FSS) functions for anisotropic three-dimensional (3D) Ising models of size L 1 × L 1 × aL 1 ( a : anisotropy parameter) are studied by Monte Carlo simulations. We study the a dependence of FSS functions of the Binder parameter g and the magnetization distribution function p ( m ). We have shown that the FSS functions for p ( m ) at the critical temperature change from a two-peak structure to a single-peak one by increasing or decreasing a from 1. We also study the FSS near the critical temperature of the layered square-lattice Ising model, when the systems have a large two-dimensional (2D) anisotropy. We have found the 3D and 2D FSS behaviour depending on the parameter which is fixed; a unified view of 3D and 2D FSS behaviour has been obtained for the anisotropic 3D Ising models.

arXiv:cond-mat/9909262•Journal of Physics A Mathematical and General•Oct 13, 1999•14 citations

Universal reduction of effective coordination number in the quasi-one-dimensional Ising model

Synge Todo

Critical temperature of quasi-one-dimensional general-spin Ising ferromagnets is investigated by means of the cluster Monte Carlo method performed on infinite-length strips, $L\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$ or $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$. We find that in the weak interchain coupling regime the critical temperature as a function of the interchain coupling is well-described by a chain mean-field formula with a reduced effective coordination number, as the quantum Heisenberg antiferromagnets recently reported by Yasuda et al. [Phys. Rev. Lett. 94, 217201 (2005)]. It is also confirmed that the effective coordination number is independent of the spin size. We show that in the weak interchain coupling limit the effective coordination number is, irrespective of the spin size, rigorously given by the quantum critical point of a spin-$1∕2$ transverse-field Ising model.

arXiv:cond-mat/0606790•Physical Review B•Sep 22, 2006•6 citations

Finite size analysis for interacting bosons at the one-two dimensional crossover

Lorenzo Pizzino, Hepeng Yao, Thierry Giamarchi

In this work, we extend the analysis of interacting bosons at 2D-1D dimensional crossover for finite size and temperature by using the field theory approach ( b o s o n i z a t i o n ) and quantum Monte Carlo simulations. Stemming from the fact that finite size low-dimensional systems are allowed only to have quasiordered phase, we consider the self-consistent harmonic approximation to compute the fraction of quasicondensate and its scaling with the system size. It allows us to understand the important role played by finite size and temperature across the dimensional crossover for deciding the condensate nature. Furthermore, we consider a mean-field approximation to compute the finite size effect on the crossover temperature for both weak and strong interactions. All the physical quantities we discuss here provide essential information for quantum gas at dimensional crossover and are directly detectable in cold atom experiments.

arXiv:2407.06634•Physical Review Research•Jan 7, 2025•2 citations

Finite-size scaling and the crossover to mean-field critical behavior in the two-dimensional Ising model with medium-ranged interactions

K. K. Mon, Kurt Binder

Critical amplitudes in finite-size scaling relations show a singular dependence on the range of the interactions, R. The respective power laws are predicted from phenomenological crossover scaling considerations. These predictions are tested by Monte Carlo simulations for medium-ranged Ising square lattices. It is speculated that some deviations between the simulation results and corresponding predictions may be due to logarithmic corrections.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Oct 1, 1993•48 citations

Wang–Landau Simulation for the Quasi-One-Dimensional Ising Model

Takayuki Tanabe, Kouichi Okunishi

We revisit the nature of the quasi-one-dimensional Ising model on the basis of Wang-Landau simulation. We introduce the density of states in the two-dimensional energy space corresponding to the intra- and inter-chain directions. We then analyze the interchain coupling dependence of the specific heat of the anistropic two-dimensional Ising model in the context of the density of states, and further discuss the size dependences of the peak temperature. We also discuss the feature of the phase transition in the three-dimensional case.

arXiv:0901.0637•Journal of the Physical Society of Japan•May 11, 2009•1 citation
We have studied the finite size effect in the quasi-one-dimensional Ising model by using a Monte Carlo simulation. A marked finite size effect was found with decreasing interchain interaction. Aside from the well-known dimensional crossover from 3D to 1D, a dimensional crossover from 3D to 2D at a crossover size L c (λ) ∼-1/(λln λ) was revealed as an origin of the finite size effect, where λ is the ratio of the interchain interaction to the intrachain one.
The finite-size scaling (FSS) functions for anisotropic three-dimensional (3D) Ising models of size L 1 × L 1 × aL 1 ( a : anisotropy parameter) are studied by Monte Carlo simulations. We study the a dependence of FSS functions of the Binder parameter g and the magnetization distribution function p ( m ). We have shown that the FSS functions for p ( m ) at the critical temperature change from a two-peak structure to a single-peak one by increasing or decreasing a from 1. We also study the FSS near the critical temperature of the layered square-lattice Ising model, when the systems have a large two-dimensional (2D) anisotropy. We have found the 3D and 2D FSS behaviour depending on the parameter which is fixed; a unified view of 3D and 2D FSS behaviour has been obtained for the anisotropic 3D Ising models.
Critical temperature of quasi-one-dimensional general-spin Ising ferromagnets is investigated by means of the cluster Monte Carlo method performed on infinite-length strips, $L\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$ or $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$. We find that in the weak interchain coupling regime the critical temperature as a function of the interchain coupling is well-described by a chain mean-field formula with a reduced effective coordination number, as the quantum Heisenberg antiferromagnets recently reported by Yasuda et al. [Phys. Rev. Lett. 94, 217201 (2005)]. It is also confirmed that the effective coordination number is independent of the spin size. We show that in the weak interchain coupling limit the effective coordination number is, irrespective of the spin size, rigorously given by the quantum critical point of a spin-1∕21∕21∕2 transverse-field Ising model.
In this work, we extend the analysis of interacting bosons at 2D-1D dimensional crossover for finite size and temperature by using the field theory approach ( b o s o n i z a t i o n ) and quantum Monte Carlo simulations. Stemming from the fact that finite size low-dimensional systems are allowed only to have quasiordered phase, we consider the self-consistent harmonic approximation to compute the fraction of quasicondensate and its scaling with the system size. It allows us to understand the important role played by finite size and temperature across the dimensional crossover for deciding the condensate nature. Furthermore, we consider a mean-field approximation to compute the finite size effect on the crossover temperature for both weak and strong interactions. All the physical quantities we discuss here provide essential information for quantum gas at dimensional crossover and are directly detectable in cold atom experiments.
We revisit the nature of the quasi-one-dimensional Ising model on the basis of Wang-Landau simulation. We introduce the density of states in the two-dimensional energy space corresponding to the intra- and inter-chain directions. We then analyze the interchain coupling dependence of the specific heat of the anistropic two-dimensional Ising model in the context of the density of states, and further discuss the size dependences of the peak temperature. We also discuss the feature of the phase transition in the three-dimensional case.