4 papers
Log-Sobolev Inequality for Wolff Dynamics and Application to the Condensation of Eigen Microstate in the 1D Ising Model
Kaiyuan Cui, Fuzhou Gong
The Wolff dynamics is a non-local Markov chain widely used for simulating the Ising model due to its effectiveness in reducing critical slowing down compared to the Glauber dynamic…
The log-Sobolev inequality and correlation functions for the renormalization of 1D Ising model
Kaiyuan Cui, Fuzhou Gong
The renormalization group (RG) method is an important tool for studying critical phenomena. In this paper, we employ stochastic analysis techniques to investigate the stochastic pa…
The behavior of renormalization and related observables
Cui Kaiyuan, Gong Fuzhou
In this paper, we introduce new reference observables to establish a scaling formula in the renormalization group equation. Using the transfer matrix method, we calculate the two p…
The local Poincare inequality of stochastic dynamic and application to the Ising model
Kaiyuan Cui, Fuzhou Gong
Inspired by the idea of stochastic quantization proposed by Parisi and Wu, we construct the transition probability matrix which plays a central role in the renormalization group th…