Magnetization distribution in the transverse Ising chain with energy flux

Details Magnetization distribution in the transverse Ising chain with energy flux Magnetization distribution in the transverse Ising chain with energy flux

2003-01-24

arxiv.org/abs/cond-mat/0301473v1

Phys. Rev. E 67, 056129 (2003)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 5 ps figures

Scientific paper

10.1103/PhysRevE.67.056129

The zero-temperature transverse Ising chain carrying an energy flux j_E is studied with the aim of determining the nonequilibrium distribution functions, P(M_z) and P(M_x), of its transverse and longitudinal magnetizations, respectively. An exact calculation reveals that P(M_z) is a Gaussian both at j_E=0 and j_E not equal 0, and the width of the distribution decreases with increasing energy flux. The distribution of the order-parameter fluctuations, P(M_x), is evaluated numerically for spin-chains of up to 20 spins. For the equilibrium case (j_E=0), we find the expected Gaussian fluctuations away from the critical point while the critical order-parameter fluctuations are shown to be non-gaussian with a scaling function Phi(x)=Phi(M_x/)=P(M_x) strongly dependent on the boundary conditions. When j_E not equal 0, the system displays long-range, oscillating correlations but P(M_x) is a Gaussian nevertheless, and the width of the Gaussian decreases with increasing j_E. In particular, we find that, at critical transverse field, the width has a j_E^(-3/8) asymptotic in the j_E -> 0 limit.

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