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 $D\leq D^{\ast}\simeq 6$ and $0<T_{c}(D)<T_{c}(d=2)$ for $D>D^{\ast}.$ Regular scaling of $ML^{β/ν}$ vs $|T-T_{c}|L^{1/ν}$ is obtained only for $% D>D^{\ast}$and the Monte Carlo effective susceptibility critical exponent $γ_{eff} (D)$ is shown to be well described by $γ(d)=β(d)[δ(d)-1]$ with $% d_{eff}(D)$ given by $d_{eff}(D)\simeq 1.5+({1/200})(D-6)$ and $β(d)=(\frac{3d%}{16}-{1/4}),$ $δ^{-1}(d)=(\frac{2d}{15}-{1/5})$, which can be understood as valid with $d_{eff}(D)$.