标题： 三维随机场伊辛模型的临界行为：双指数标度还是一阶相变？ 显示英文标题

标题： Critical Behavior of the 3d Random Field Ising Model: Two-Exponent Scaling or First Order Phase Transition?

摘要： 在广泛的蒙特卡洛模拟中，研究了三维随机磁场伊辛模型的相变。通过有限尺寸缩放确定了临界指数的值。对于高斯分布的随机场，发现在临界温度下关联长度$\xi$以指数$\nu=1.1\pm0.2$发散，并且连接磁化率$\chi\sim\xi^{2-\eta}$与$\eta=0.50\pm0.05$，非连接磁化率$\chi_{\rm dis}\sim\xi^{4-\bar{\eta}}$与$\bar{\eta}=1.03\pm0.05$。 结合振幅比 $A=\lim_{T\to T_c}\chi_{\rm dis}/\chi^2(h_r/T)^2$接近于一，这进一步支持了双指数标度情景，意味着 $\bar{\eta}=2\eta$。 磁化强度在相变时表现出不连续性，即 $\beta=0$，表明是一种一级相变。 然而，没有发现比热的发散，特别是没有潜热。 此外，磁化强度的概率分布也没有显示出多峰结构，这是典型的一级相变点处相共存的特征。 显示英文摘要

摘要： In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the random fields it is found that the correlation length $\xi$ diverges with an exponent $\nu=1.1\pm0.2$ at the critical temperature and that $\chi\sim\xi^{2-\eta}$ with $\eta=0.50\pm0.05$ for the connected susceptibility and $\chi_{\rm dis}\sim\xi^{4-\bar{\eta}}$ with $\bar{\eta}=1.03\pm0.05$ for the disconnected susceptibility. Together with the amplitude ratio $A=\lim_{T\to T_c}\chi_{\rm dis}/\chi^2(h_r/T)^2$ being close to one this gives further support for a two exponent scaling scenario implying $\bar{\eta}=2\eta$. The magnetization behaves discontinuously at the transition, i.e. $\beta=0$, indicating a first order transition. However, no divergence for the specific heat and in particular no latent heat is found. Also the probability distribution of the magnetization does not show a multi-peak structure that is characteristic for the phase-coexistence at first order phase transition points.