Finite-size corrections to scaling of the magnetization distribution in the two-dimensional XY model at zero temperature

G. Palma, F. Niedermayer, Z. Rácz, A. Riveros, D. Zambrano

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Abstract

The zero-temperature, classical XY model on an L×L square lattice is studied by exploring the distribution ΦL(y) of its centered and normalized magnetization y in the large-L limit. An integral representation of the cumulant generating function, known from earlier works, is used for the numerical evaluation of ΦL(y), and the limit distribution ΦL→∞(y)=Φ0(y) is obtained with high precision. The two leading finite-size corrections ΦL(y)-Φ0(y)≈a1(L)Φ1(y)+a2(L)Φ2(y) are also extracted both from numerics and from analytic calculations. We find that the amplitude a1(L) scales as ln(L/L0)/L2 and the shape correction function Φ1(y) can be expressed through the low-order derivatives of the limit distribution, Φ1(y)=[yΦ0(y)+Φ0′(y)]′. Thus, Φ1(y) carries the same universal features as the limit distribution and can be used for consistency checks of universality claims based on finite-size systems. The second finite-size correction has an amplitude a2(L)∝1/L2 and one finds that a2Φ2(y)a1Φ1(y) already for small system size (L>10). We illustrate the feasibility of observing the calculated finite-size corrections by performing simulations of the XY model at low temperatures, including T=0.

Original languageEnglish
Article number022145
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume94
Issue number2
DOIs
Publication statusPublished - Aug 29 2016

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Corrections to Scaling
XY Model
Finite-size Scaling
two dimensional models
Magnetization
scaling
Limit Distribution
magnetization
Zero
temperature
Cumulants
Numerics
Square Lattice
Integral Representation
Universality
Generating Function
Derivative
evaluation
Evaluation
Simulation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Finite-size corrections to scaling of the magnetization distribution in the two-dimensional XY model at zero temperature. / Palma, G.; Niedermayer, F.; Rácz, Z.; Riveros, A.; Zambrano, D.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 94, No. 2, 022145, 29.08.2016.

Research output: Contribution to journalArticle

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