Critical behavior of the two-dimensional XY model

Gupta, R; Baillie, C F

doi:10.1103/PhysRevB.45.2883

Title: Critical behavior of the two-dimensional XY model

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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:

Gupta, R ^[1]; Baillie, C F ^[2]

T-8, MS-B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
Physics Department, University of Colorado, Boulder, Colorado 80309 (United States)

Publication Date:: 1992-02-01

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.

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                    Gupta, R, & Baillie, C F. Critical behavior of the two-dimensional XY model.  United States.  https://doi.org/10.1103/PhysRevB.45.2883

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                    Gupta, R, and Baillie, C F. 1992.  
        "Critical behavior of the two-dimensional XY model".  United States.  https://doi.org/10.1103/PhysRevB.45.2883.

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@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},

  url          = {https://www.osti.gov/biblio/7276693},
  journal      = {Physical Review, B: Condensed Matter; (United States)},

  issn         = {0163-1829},

  number       = ,

  volume       = 45:6,

  place        = {United States},

  year         = {1992},

  month        = {2}

}

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