论文标题
$ P $ -Spin球形平均场旋转玻璃模型的Tap Energy的相图
Phase diagram for the tap energy of the $p$-spin spherical mean field spin glass model
论文作者
论文摘要
我们解决了与球形纯$ p $ -spin平均田间自旋玻璃哈密顿量相关的thou thou-anderson-palmer（TAP）变异原理，并提供了详细的相图。 在高温阶段，变异原理的最大是模型的退火自由能。在低温阶段，我们给出的公式的最大值严格较小。 高温阶段由三个子量组成。 （1）在第一阶段$ m = 0 $是唯一相关的TAP最大化器。 （2）在第二阶段，有很多Tap Maximizer指数，但$ M = 0 $仍然占主导地位。 （3）在第三阶段，在所谓的动态相变之后，$ m = 0 $不再是相关的TAP最大化器，并且呈指数级的许多非零相关的TAP解决方案加起来可以提供退火的自由能。 最后，在低温阶段，近似最大的TAP能量占主导地位的次指数数量最大化。
We solve the Thouless-Anderson-Palmer (TAP) variational principle associated to the spherical pure $p$-spin mean field spin glass Hamiltonian and present a detailed phase diagram. In the high temperature phase the maximum of variational principle is the annealed free energy of the model. In the low temperature phase the maximum, for which we give a formula, is strictly smaller. The high temperature phase consists of three subphases. (1) In the first phase $m=0$ is the unique relevant TAP maximizer. (2) In the second phase there are exponentially many TAP maximizers, but $m=0$ remains dominant. (3) In the third phase, after the so called dynamic phase transition, $m=0$ is no longer a relevant TAP maximizer, and exponentially many non-zero relevant TAP solutions add up to give the annealed free energy. Finally in the low temperature phase a subexponential number of TAP maximizers of near-maximal TAP energy dominate.
