Rounding effects of quenched randomness on first-order phase transitions
Rounding effects of quenched randomness on first-order phase transitions
复制标题
淬火随机性对一阶相变的舍入效应
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
J. Wehr
中科院分区：
文献类型：
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作者：
M. Aizenman;J. Wehr
在一个均匀系统中的冻结无序，是由具有随机系数的相互作用项来模拟的，由独立的随机变量给出，其分布是不变的。对于这样的系统，它被证明，ind=2维，可以没有一阶相变与耦合到随机化参数的量的热平均值的不连续性。在O（N）的连续子群作用下（随机）不变的系统中，相当于连续对称破缺的不连续性被维数d = 4的随机性所抑制。在随机场伊辛模型中发现了具体的含义，我们得出结论，ind=2维（β，h）吉布斯态对几乎所有的场配置都是唯一的，在随机键波茨模型中，一般现象表现在相变点的潜热消失。用Imry和Ma [1]的论点解释了这一结果。证据涉及自由能差异的波动分析，这是（使用鞅技术）是高斯在适当的规模。
Frozen-in disorder in an otherwise homogeneous system, is modeled by interaction terms with random coefficients, given by independent random variables with a translation-invariant distribution. For such systems, it is proven that ind=2 dimensions there can be no first-order phase transition associated with discontinuities in the thermal average of a quantity coupled to the randomized parameter. Discontinuities which would amount to a continuous symmetry breaking, in systems which are (stochastically) invariant under the action of a continuous subgroup ofO(N), are suppressed by the randomness in dimensionsd≦4. Specific implications are found in the Random-Field Ising Model, for which we conclude that ind=2 dimensions at all (β,h) the Gibbs state is unique for almost all field configurations, and in the Random-Bond Potts Model where the general phenomenon is manifested in the vanishing of the latent heat at the transition point. The results are explained by the argument of Imry and Ma [1]. The proofs involve the analysis of fluctuations of free energy differences, which are shown (using martingale techniques) to be Gaussian on the suitable scale.