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Title: Critical behavior of the two-dimensional 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 Kosterlitz-Thouless (KT) singularity over a second-order transition; however, unconstrained four-parameter 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 spin-wave phase using Monte Carlo renormalization-group and finite-size-scaling 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 dilute-gas approximation breaks down.

Authors:
 [1];  [2]
  1. T-8, MS-B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
  2. Physics Department, University of Colorado, Boulder, Colorado 80309 (United States)
Publication Date:
OSTI Identifier:
7276693
DOE Contract Number:  
FG03-85ER25009
Resource Type:
Journal Article
Journal Name:
Physical Review, B: Condensed Matter; (United States)
Additional Journal Information:
Journal Volume: 45:6; Journal ID: ISSN 0163-1829
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; STATISTICAL MODELS; MAGNETIC SUSCEPTIBILITY; SPECIFIC HEAT; COMPUTERIZED SIMULATION; KOSTERLITZ-THOULESS 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 two-dimensional XY model. United States: N. p., 1992. Web. doi:10.1103/PhysRevB.45.2883.
Gupta, R, & Baillie, C F. Critical behavior of the two-dimensional XY model. United States. doi:10.1103/PhysRevB.45.2883.
Gupta, R, and Baillie, C F. Sat . "Critical behavior of the two-dimensional XY model". United States. doi:10.1103/PhysRevB.45.2883.
@article{osti_7276693,
title = {Critical behavior of the two-dimensional 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 Kosterlitz-Thouless (KT) singularity over a second-order transition; however, unconstrained four-parameter 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 spin-wave phase using Monte Carlo renormalization-group and finite-size-scaling 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 dilute-gas approximation breaks down.},
doi = {10.1103/PhysRevB.45.2883},
journal = {Physical Review, B: Condensed Matter; (United States)},
issn = {0163-1829},
number = ,
volume = 45:6,
place = {United States},
year = {1992},
month = {2}
}