Gibbs measures and semiclassical approximations to action minimizing measures

Gibbs-non-Gibbs transition in the fuzzy Potts models with a Kac-type interaction: Closing the Ising gap

We complete the investigation of the Gibbs properties of the fuzzy Potts model on the d-dimensional torus with Kac interaction which was started by Jahnel and one of the authors. As our main result of the present paper, we extend the previous sharpness result of mean-field bounds to cover all possible cases of fuzzy transformations, allowing also for the occurrence of Ising classes. The closing of this previously left open Ising-gap involves an analytical argument showing uniqueness of minimizing profiles for certain non-homogeneous conditional variational problems.

A large-deviation view on dynamical Gibbs-non-Gibbs transitions

We develop a space-time large-deviation point of view on Gibbs-non-Gibbs transitions in spin systems subject to a stochastic spin-flip dynamics. Using the general theory for large deviations of functionals of Markov processes outlined in Feng and Kurtz [11], we show that the trajectory under the spin-flip dynamics of the empirical measure of the spins in a large block in Z^d satisfies a large deviation principle in the limit as the block size tends to infinity. The associated rate function can be computed as the action functional of a Lagrangian that is the Legendre transform of a certain non-…

从多体量子吉布斯态导出$Φ^4_3$理论

$Φ^4_3$ Theory from many-body quantum Gibbs states

本文从多体量子吉布斯态出发，通过半经典极限严格导出环面上的$Φ^4_3$测度，并利用副控制演算新技术以非局域Hartree测度逼近目标测度，揭示了临界温度附近玻色-爱因斯坦凝聚的形成机制。

TAP free energy, spin glasses, and variational inference

We consider the Sherrington-Kirkpatrick model of spin glasses with ferromagnetically biased couplings. For a specific choice of the couplings mean, the resulting Gibbs measure is equivalent to the Bayesian posterior for a high-dimensional estimation problem known as `$Z_2$ synchronization'. Statistical physics suggests to compute the expectation with respect to this Gibbs measure (the posterior mean in the synchronization problem), by minimizing the so-called Thouless-Anderson-Palmer (TAP) free energy, instead of the mean field (MF) free energy. We prove that this identification is correct, pr…

群平均马尔可夫链II：在有限状态空间中调节群作用

Group-averaged Markov chains II: tuning of group action in finite state space

本文研究了群平均马尔可夫链，分析了轨道核及其混合方法，并提出调节群作用的启发式方法，展示了GPG在信息投影中的应用及在不同模型中的混合性能。