Probability distribution of magnetization in the one-dimensional Ising model: Effects of boundary conditions

T. Antal, M. Droz, Z. Rácz

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T → 0), the size of the system going to infinity (N →∞ ) while N[1 - tanh(J/k BT)] is kept finite (J being the nearest neighbour coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.

Original languageEnglish
Pages (from-to)1465-1478
Number of pages14
JournalJournal of Physics A: Mathematical and General
Volume37
Issue number5
DOIs
Publication statusPublished - Feb 6 2004

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Ising model
Scaling Function
One-dimensional Model
Magnetization
Probability distributions
Ising Model
Probability Distribution
Boundary conditions
boundary conditions
scaling
magnetization
free boundaries
Finite-size Scaling
Periodic Boundary Conditions
Free Boundary
Mean Square
infinity
Nearest Neighbor
Infinity
Fluctuations

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Probability distribution of magnetization in the one-dimensional Ising model : Effects of boundary conditions. / Antal, T.; Droz, M.; Rácz, Z.

In: Journal of Physics A: Mathematical and General, Vol. 37, No. 5, 06.02.2004, p. 1465-1478.

Research output: Contribution to journalArticle

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