Effective Critical Exponents of Ising Strips D*L with D<<L

TL;DR

This study uses Monte Carlo simulations to analyze phase transitions in Ising strips, revealing how effective critical exponents depend on the strip width and establishing a relationship with an effective dimension.

Contribution

It introduces a model for effective critical exponents in Ising strips, linking them to an effective dimension that varies with strip width, D.

Findings

Critical temperature T_c(D) is zero for D ≤ 6.

Regular scaling occurs only for D > 6.

Effective susceptibility exponent γ_eff(D) fits a dimension-dependent formula.

Abstract

Monte Carlo data simulating phase transitions in Ising strips $D\times L,$ ($D\llL) $ with periodic boundary conditions show that $T_{c}(D)=0$ for $D\leq D^{\ast}\simeq 6$ and $0<T_{c}(D)<T_{c}(d=2)$ for $D>D^{\ast}.$ Regular scaling of $ML^{\beta /\nu}$ vs $|T-T_{c}|L^{1/\nu}$ is obtained only for $% D>D^{\ast}$and the Monte Carlo effective susceptibility critical exponent $\gamma_{eff} (D)$ is shown to be well described by $\gamma (d)=\beta (d)[\delta (d)-1]$ with $% d_{eff}(D)$ given by $d_{eff}(D)\simeq 1.5+({1/200})(D-6)$ and $\beta (d)=(\frac{3d%}{16}-{1/4}),$ $\delta ^{-1}(d)=(\frac{2d}{15}-{1/5})$, which can be understood as valid with $d_{eff}(D)$.