Critical behavior of the twodimensional XY model
Abstract
We present detailed Monte Carlo results for the susceptibility {chi}, correlation length {xi}, and specific heat {ital C}{sub {ital v}} for the {ital XY} model. The simulations are done on 64{sup 2}, 128{sup 2}, 256{sup 2}, and 512{sup 2} lattices over the temperature range 0.98{le}{ital T}{le}1.43 corresponding to 2{lt}{xi}{lt}70. Fits to {chi} and {xi} data favor a KosterlitzThouless (KT) singularity over a secondorder transition; however, unconstrained fourparameter KT fits do not confirm the predicted values {nu}=0.5 and {eta}=0.25. Our best estimate, {ital T}{sub {ital c}}=0.894(5), is obtained using KT fits with {nu} fixed at 0.5. The exponent {eta} is calculated as a function of temperature in the spinwave phase using Monte Carlo renormalizationgroup and finitesizescaling methods. Both methods give consistent results and we find {eta}{approx}0.235 at {ital T}=0.894. We also present results for the behavior of vortex density across the transition and exhibit how the dilutegas approximation breaks down.
 Authors:

 T8, MSB285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
 Physics Department, University of Colorado, Boulder, Colorado 80309 (United States)
 Publication Date:
 OSTI Identifier:
 7276693
 DOE Contract Number:
 FG0385ER25009
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review, B: Condensed Matter; (United States)
 Additional Journal Information:
 Journal Volume: 45:6; Journal ID: ISSN 01631829
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; STATISTICAL MODELS; MAGNETIC SUSCEPTIBILITY; SPECIFIC HEAT; COMPUTERIZED SIMULATION; KOSTERLITZTHOULESS THEORY; MONTE CARLO METHOD; SCALING; TEMPERATURE DEPENDENCE; MAGNETIC PROPERTIES; MATHEMATICAL MODELS; PHYSICAL PROPERTIES; SIMULATION; THERMODYNAMIC PROPERTIES; 665000*  Physics of Condensed Matter (1992)
Citation Formats
Gupta, R, and Baillie, C F. Critical behavior of the twodimensional XY model. United States: N. p., 1992.
Web. doi:10.1103/PhysRevB.45.2883.
Gupta, R, & Baillie, C F. Critical behavior of the twodimensional XY model. United States. https://doi.org/10.1103/PhysRevB.45.2883
Gupta, R, and Baillie, C F. 1992.
"Critical behavior of the twodimensional XY model". United States. https://doi.org/10.1103/PhysRevB.45.2883.
@article{osti_7276693,
title = {Critical behavior of the twodimensional XY model},
author = {Gupta, R and Baillie, C F},
abstractNote = {We present detailed Monte Carlo results for the susceptibility {chi}, correlation length {xi}, and specific heat {ital C}{sub {ital v}} for the {ital XY} model. The simulations are done on 64{sup 2}, 128{sup 2}, 256{sup 2}, and 512{sup 2} lattices over the temperature range 0.98{le}{ital T}{le}1.43 corresponding to 2{lt}{xi}{lt}70. Fits to {chi} and {xi} data favor a KosterlitzThouless (KT) singularity over a secondorder transition; however, unconstrained fourparameter KT fits do not confirm the predicted values {nu}=0.5 and {eta}=0.25. Our best estimate, {ital T}{sub {ital c}}=0.894(5), is obtained using KT fits with {nu} fixed at 0.5. The exponent {eta} is calculated as a function of temperature in the spinwave phase using Monte Carlo renormalizationgroup and finitesizescaling methods. Both methods give consistent results and we find {eta}{approx}0.235 at {ital T}=0.894. We also present results for the behavior of vortex density across the transition and exhibit how the dilutegas approximation breaks down.},
doi = {10.1103/PhysRevB.45.2883},
url = {https://www.osti.gov/biblio/7276693},
journal = {Physical Review, B: Condensed Matter; (United States)},
issn = {01631829},
number = ,
volume = 45:6,
place = {United States},
year = {1992},
month = {2}
}