Universality aspects of the trimodal random-field Ising model

• Published in: The European physical journal. B, Condensed matter physics Vol. 85; no. 10
• Main Authors: Fytas, N.G., Theodorakis, P.E., Georgiou, I.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-10-2012; EDP Sciences; Springer
• Subjects: Algorithms; Analysis; Complex Systems; Condensed Matter Physics; Exact sciences and technology; Fluid- and Aerodynamics; Lattice theory and statistics (ising, potts, etc.); Physics; Physics and Astronomy; Regular Article; Solid State Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Statistical and Nonlinear Physics; Universality class; Random field; Finite size effect; Fluctuations; Scaling laws; Ising model; Order parameters; Graph theory; Critical phenomena; Critical exponents
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2012-30731-8

.
We investigate the critical properties of the
d
 = 3 random-field Ising model with an equal-weight trimodal distribution at zero temperature. By implementing suitable graph-theoretical algorithms, we compute large ensembles of ground states for several values of the disorder strength
h
and system sizes up to
N
 = 128
3
. Using a new approach based on the sample-to-sample fluctuations of the order parameter of the system and proper finite-size scaling techniques we estimate the critical disorder strength
h
c
 = 2.747(3) and the critical exponents of the correlation length
ν
 = 1.34(6) and order parameter
β
 = 0.016(4). These estimates place the model into the universality class of the corresponding Gaussian random-field Ising model.