On the stability of the quenched state in mean-field spin-glass models
On the stability of the quenched state in mean-field spin-glass models
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DOI：
10.1023/a:1023080223894
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发表时间：
1998-09-01
影响因子：
1.6
通讯作者：
Contucci, P
中科院分区：
文献类型：
--
作者：
Aizenman, M;Contucci, P
虽然已经注意到，旋转玻璃模型的吉布斯状态对温度具有不稳定的依赖性，但人们可能期望该疾病的平均值会产生连续变化的“淬火状态”。温度中这种连续性的假设意味着在无限体积的限制中，状态在吉布斯度量的一类变形下是稳定的。巴黎安萨兹（Ansatz）以及更广泛的平稳性属性满足了这种情况。稳定性条件具有等效的表达方式，即淬灭自由能的边际添加性。连续性假设的含义包括对重叠分布的限制，这表示是无限重叠多项式收集的期望值消失。多项式可以借助实重计算，其中副本的数量被取为零。
While the Gibbs states of spin-glass models have been noted to have an erratic dependence on temperature, one may expect the mean over the disorder to produce a continuously varying "quenched state." The assumption of such continuity in temperature implies that in the infinite-volume limit the state is stable under a class of deformations of the Gibbs measure. The condition is satisfied by the Parisi Ansatz, along with an even broader stationarity property. The stability conditions have equivalent expressions as marginal additivity of the quenched free energy. Implications of the continuity assumption include constraints on the overlap distribution, which are expressed as the vanishing of the expectation value for an infinite collection of multi- overlap polynomials. The polynomials can be computed with the aid of a real-replica calculation in which the number of replicas is taken to zero.