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

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 $D\le D^{\ast }\simeq 6$ and $0<T_c(D)<T_c(d=2)$ for $D>D^{\ast }.$ Regular scaling of $M{L}^{\beta /\nu }$ vs $|T-T_c|L^{1/\nu }$ is obtained only for 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 given by $d_{eff}(D)\simeq 1.5+(1/200)(D-6)$ and $β(d)=(\frac{3d%}{16}-{1/4}),$ ${\delta }^{-1}(d)=(\frac{2d}{15}-1/5)$, which can be understood as valid with $d_{eff}(D)$.

6 pages, 7 figures