Interpretation of topologically restricted measurements in lattice σ-models

30th Annual Meeting of the Division of Particles and Fields (DPyC) of the Mexican Physical Society

Bautista, Irais^1 ; Bietenholz, Wolfgang^1 ; Gerber, Urs^1,2 ; Hofmann, Christoph P.^3 ; Mejia-Diaz, Héctor^1 ; Prado, Lilian^1

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Ciudad de México

C.P. 04510, Mexico^1

Instituto de Fisica y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Apdo. Postal 2-82, Michoacán, Morelia

C.P. 58040, Mexico^2

Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima

C.P. 28045, Mexico^3

关键词: Nonlinear sigma model;    Numerical tests;    Sigma model;    Topological charge densities;    Topological charges;    Topological susceptibility;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/761/1/012087/pdf
DOI  :  10.1088/1742-6596/761/1/012087

来源: IOP

【 摘 要 】

We consider models with topological sectors, and difficulties with their Monte Carlo simulation. In particular we are concerned with the situation where a simulation has an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are possible only within single topological sectors. The challenge is to assemble such restricted measurements to obtain an approximation for the full-fledged result, which corresponds to the correct sampling over the entire set of configurations. Under certain conditions this is possible, and it provides in addition an estimate for the topological susceptibility χt. Moreover, the evaluation of χt might be feasible even from data in just one topological sector, based on the correlation of the topological charge density. Here we present numerical test results for these techniques in the framework of non-linear σ-models.