Grassmannization of the 3D Ising Model

Proceedings

L. Pollet¹  E. Martello²  G. G. N. Angilella² 

[1] Department of Physics, Arnold Sommerfeld Center for Theoretical Physics, Theresienstrasse 37, D-80333 Munich, Germany;Dipartimento di Fisica e Astronomia “Ettore Majorana”, Università di Catania, Via S. Sofia, 64, I-95123 Catania, Italy;

关键词: Ising model;    Grassmann variables;    Many-body theory;    Feynman diagrams;   

DOI  :  10.3390/proceedings2019012020

来源: DOAJ

【 摘 要 】

The Ising model is a reference model for applications in quantum computing, and is often used as a benchmark for numerical simulations. Classical Monte Carlo (MC) simulations are carried out only for finite-size lattices, and the result is generalized to the infinite-size lattice by data collapse. Lattice gauge techniques are diagrammatic techniques, that already work in the thermodynamic limit, and in general simulate link variables using classical MC, and Fermions as determinants. This leads to the infamous sign problem. In order to solve it, one replaces link variables with a Bosonic field, but it may have zero convergence radius. Here, link variables are replaced by a Grassmannian field. An algorithm is thus constructed, that makes it possible to obtain an expansion of the susceptibility, through which the values for the critical temperature and critical index $\gamma$ are evaluated, respectively, within 1.6% and 5.4% of their accepted values.

【 授权许可】

Unknown