Continuous-Mixture Autoregressive Networks Learning the Kosterlitz–Thouless Transition
Lingxiao Wang1,2 , Yin Jiang3* , Lianyi He2* , and Kai Zhou1*
1 Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main, Germany2 State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China3 Department of Physics, Beihang University, Beijing 100191, China
Abstract ：We develop deep autoregressive networks with multi channels to compute many-body systems with continuous spin degrees of freedom directly. As a concrete example, we demonstrate the two-dimensional XY model with the continuous-mixture networks and rediscover the Kosterlitz–Thouless (KT) phase transition on a periodic square lattice. Vortices characterizing the quasi-long range order are accurately detected by the generative model. By learning the microscopic probability distributions from the macroscopic thermal distribution, the networks are trained as an efficient physical sampler which can approximate the free energy and estimate thermodynamic observables unbiasedly with importance sampling. As a more precise evaluation, we compute the helicity modulus to determine the KT transition temperature. Although the training process becomes more time-consuming with larger lattice sizes, the training time remains unchanged around the KT transition temperature. The continuous-mixture autoregressive networks we developed thus can be potentially used to study other many-body systems with continuous degrees of freedom.
收稿日期: 2022-08-05
出版日期: 2022-12-02
:
05.10.-a
(Computational methods in statistical physics and nonlinear dynamics)
05.70.Fh
(Phase transitions: general studies)
02.70.-c
(Computational techniques; simulations)
05.70.-a
(Thermodynamics)
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2022, Vol. 39 
