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

Monte Carlo data simulating phase transitions in Ising strips $D\times L,$ ($D\text{llL})$ 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 $M{L}^{\beta \mathrm{/}\nu }$ vs $\mathrm{\mid }T-T_c\mathrm{\mid }{L}^{1\mathrm{/}\nu }$ is obtained only for $% D>D^{\ast}$andtheMonteCarloeffectivesusceptibilitycriticalexponent$\gamma_{eff} (D)$isshowntobewelldescribedby$\gamma (d)=\beta (d)[\delta (d)-1]$with$% d_{eff}(D)$givenby$d_{eff}(D)\simeq 1.5+({1/200})(D-6)$and$\beta (d)=(\frac{3d%}{16}-{1/4}),$ $\delta ^{-1}(d)=(\frac{2d}{15}-{1/5})$,whichcanbeunderstoodasvalidwith$d_{eff}(D)$.