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Title: Controlling sign problems in spin models using tensor renormalization

Abstract

We consider the sign problem for classical spin models at complex $$\beta =1/g_0^2$$ on $$L\times L$$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$$\beta$$ than the reweighting Monte Carlo method. For the Ising model with complex $$\beta$$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $$L\times L$$ lattices when the number of states $$D_s$$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

Authors:
 [1];  [2];  [1];  [3];  [3];  [3];  [3];  [1]
  1. Iowa U.
  2. Colorado U.
  3. Beijing, Inst. Phys.
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1333185
Report Number(s):
FERMILAB-PUB-13-394-T; arXiv:1309.6623
Journal ID: ISSN 2470-0010; 1255437
DOE Contract Number:  
AC02-07CH11359
Resource Type:
Journal Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 89; Journal Issue: 1; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Denbleyker, Alan, Liu, Yuzhi, Meurice, Y., Qin, M. P., Xiang, T., Xie, Z. Y., Yu, J. F., and Zou, Haiyuan. Controlling sign problems in spin models using tensor renormalization. United States: N. p., 2014. Web. doi:10.1103/PhysRevD.89.016008.
Denbleyker, Alan, Liu, Yuzhi, Meurice, Y., Qin, M. P., Xiang, T., Xie, Z. Y., Yu, J. F., & Zou, Haiyuan. Controlling sign problems in spin models using tensor renormalization. United States. https://doi.org/10.1103/PhysRevD.89.016008
Denbleyker, Alan, Liu, Yuzhi, Meurice, Y., Qin, M. P., Xiang, T., Xie, Z. Y., Yu, J. F., and Zou, Haiyuan. 2014. "Controlling sign problems in spin models using tensor renormalization". United States. https://doi.org/10.1103/PhysRevD.89.016008. https://www.osti.gov/servlets/purl/1333185.
@article{osti_1333185,
title = {Controlling sign problems in spin models using tensor renormalization},
author = {Denbleyker, Alan and Liu, Yuzhi and Meurice, Y. and Qin, M. P. and Xiang, T. and Xie, Z. Y. and Yu, J. F. and Zou, Haiyuan},
abstractNote = {We consider the sign problem for classical spin models at complex $\beta =1/g_0^2$ on $L\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$\beta$ than the reweighting Monte Carlo method. For the Ising model with complex $\beta$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $L\times L$ lattices when the number of states $D_s$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.},
doi = {10.1103/PhysRevD.89.016008},
url = {https://www.osti.gov/biblio/1333185}, journal = {Physical Review D},
issn = {2470-0010},
number = 1,
volume = 89,
place = {United States},
year = {Thu Jan 09 00:00:00 EST 2014},
month = {Thu Jan 09 00:00:00 EST 2014}
}