2003/01/24 by V. Eisler, Viktor Eisler, Zoltàn Ràcz +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · Medicine · Physics and Astronomy · #Complex Systems and Time Series Analysis #Condensed matter physics #Distribution (mathematics) #Flux (metallurgy) #Ising model #Magnetic field #Magnetization #Materials science #Mathematical analysis #Mathematics #Medicine #Physics #Quantum many-body systems #Quantum mechanics #Radiology #Statistical physics #Theoretical and Computational Physics #Transverse plane #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.67.056129
published as Phys. Rev. E 67, 056129 (2003) · 8 pages, 5 ps figures
arxiv created 2003/01/24 · openalex publication_date 2003/05/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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(Mx) of its transverse and longitudinal magnetizations, respectively. An exact calculation reveals that P(M(z)) is a Gaussian both at j(E)=0 and at j(E) not equal to 0, and the width of the distribution decreases with increasing energy flux. The distribution of the order-parameter fluctuations, P(Mx), 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)/<Mx>)=<Mx>P(Mx) strongly dependent on the boundary conditions. When j(E) not equal to 0, the system displays long-range, oscillating correlations but P(Mx) 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(-3/8)(E) asymptotic in the j(E)-->0 limit.