高階張量重整化群在二維橫場易辛模型的應用

Abstract

本研究深入探討了二維橫場易辛模型（2D Transverse Field Ising Model, 2D TFIM）在正方晶格上的相變行為，透過張量網路方法來求得其磁化率的高階動差。易辛模型作為凝態物理中的一個基本模型，已被廣泛用於研究鐵磁性和反鐵磁性等物質的相變。本次研究透過二維的無限時間演化區塊分解(2D Infinite Time-Evolving Block Decimation, 2D ITEBD )[1]來得到二維橫場易辛模型的基態，再透過高階張量重整化群(Higher-Order Tensor Renormalization Group ,HOTRG) [2]來計算磁化率的高階矩並且透過磁化率的高階矩來計算Binder ratio來決定系統的相變點。在未來可以計算其他熱力學性質如相關長度和比熱，更進一步完整這份研究。

This study delves into the phase transition behavior of the two-dimensional Transverse Field Ising Model (2D TFIM) on a square lattice. The higher-order moments of the magnetization are obtained through the tensor network method. The Ising model, serving as a fundamental model in condensed matter physics, has been widely used to investigate the phase transitions of materials such as ferromagnets and antiferromagnets. In this research, the ground state of the 2D TFIM is obtained through two-dimensional infinite-time evolution block decimation(2D ITEBD) [1]. Subsequently, the higher-order moments of the magnetization are calculated using the Higher-Order Tensor Renormalization Group (HOTRG). [2] The Binder ratio is determined through these higher-order moments of the magnetization to identify the system's phase transition point. In the future, other thermodynamic properties such as the correlation length and the specific heat can be computed to further enhance the comprehensiveness of this study.