{
  "id": "1406.7491",
  "version": "v2",
  "published": "2014-06-29T11:33:53.000Z",
  "updated": "2015-05-14T06:25:46.000Z",
  "title": "Corrections to finite--size scaling in the phi^4 model on square lattices",
  "authors": [
    "J. Kaupuzs",
    "R. V. N. Melnik",
    "J. Rimsans"
  ],
  "comment": "25 pages, 8 figures, 8 tables. This is a completed version, including a new theorem and new numerical data and analysis",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Corrections to scaling in the two-dimensional scalar phi^4 model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L (from 4 to 1536) and different values of the phi^4 coupling constant lambda, i.~e., lambda = 0.1, 1, 10. According to our analysis, amplitudes of the nontrivial correction terms with the correction-to-scaling exponents omega_l < 1 become small when approaching the Ising limit (lambda --> infinity), but such corrections generally exist in the 2D phi^4 model. Analytical arguments show the existence of corrections with the exponent 3/4. The numerical analysis suggests that there exist also corrections with the exponent 1/2 and, very likely, also corrections with the exponent about 1/4, which are detectable at lambda = 0.1. The numerical tests clearly show that the structure of corrections to scaling in the 2D phi^4 model differs from the usually expected one in the 2D Ising model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-29T11:33:53.000Z",
      "abstract": "Corrections to scaling in the two-dimensional scalar phi^4 model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L (from L=4 to L=1536) and different values of the phi^4 coupling constant lambda, i.~e., lambda = 0.1, 1, 10. According to our analysis, amplitudes of the nontrivial correction terms with the correction-to-scaling exponents omega_l < 1 become small when approaching the Ising limit (lambda -> infinity), but such corrections generally exist in the 2D phi^4 model. Analytical arguments show the existence of corrections with the exponent 3/4. The numerical analysis, supported by arguments of the conformal field theory, suggests that there exists also a correction with the exponent 1/2, which is detectable at lambda = 0.1. We have tested the consistency of susceptibility data with corrections, represented by an expansion in powers of L^{-1/4}. We conclude that a correction with exponent omega=1/4, probably, also exists.",
      "comment": "13 pages, 4 figures, 8 tables",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-05-14T06:25:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "square lattices",
      "finite-size scaling",
      "conformal field theory",
      "nontrivial correction terms",
      "analytical arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.7491K"
    }
  }
}