论文标题
一个步骤的对称性破裂和两个温度之间的重叠
One step replica symmetry breaking and overlaps between two temperatures
论文作者
论文摘要
我们获得了在不同温度下同一随机能量模型（REM）的两个副本之间重叠的平均分布的精确分析表达。我们量化了非自动平均效应，并为在热力学极限中重叠分布中的波动计算提供了精确的方法。我们表明，重叠概率满足了复发关系，将Ghirlanda-Guerra身份推广到两个温度。 我们还使用复制方法分析了两个温度REM。重叠概率的副本表达式满足与确切形式相同的复发关系。我们展示了对巴黎复制对称破坏Ansatz的概括与我们的副本表达式一致。这种概括的关键方面是，即使在热力学极限下，我们也必须允许复制块大小的波动。这与单个温度案例形成鲜明对比，在单个温度情况下，极端条件在热力学极限内导致固定块大小。最后，我们分析了我们广义的巴黎安萨兹（Ansatz）中块大小的波动，并表明它们可能具有负方差。
We obtain an exact analytic expression for the average distribution, in the thermodynamic limit, of overlaps between two copies of the same random energy model (REM) at different temperatures. We quantify the non-self averaging effects and provide an exact approach to the computation of the fluctuations in the distribution of overlaps in the thermodynamic limit. We show that the overlap probabilities satisfy recurrence relations that generalise Ghirlanda-Guerra identities to two temperatures. We also analyse the two temperature REM using the replica method. The replica expressions for the overlap probabilities satisfy the same recurrence relations as the exact form. We show how a generalisation of Parisi's replica symmetry breaking ansatz is consistent with our replica expressions. A crucial aspect to this generalisation is that we must allow for fluctuations in the replica block sizes even in the thermodynamic limit. This contrasts with the single temperature case where the extremal condition leads to a fixed block size in the thermodynamic limit. Finally, we analyse the fluctuations of the block sizes in our generalised Parisi ansatz and show that in general they may have a negative variance.
