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

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

2003-08-21

arxiv.org/abs/cond-mat/0308442v1

J.Phys.A: Math.Gen. 37, 1465-78 (2004)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 5 figures

Scientific paper

10.1088/0305-4470/37/5/001

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 -> oo) while N[1-tanh(J/k_BT)] is kept finite (J being the nearest neighbor 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.

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