Regensburg 2013 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 33: Poster II

DY 33.60: Poster

Donnerstag, 14. März 2013, 17:00–19:00, Poster C

Ground states of 1D long-range random-field Ising magnets — •Timo Dewenter and Alexander K. Hartmann — Institut für Physik, Carl von Ossietzky Universität Oldenburg

In random-field Ising magnets (RFIMs) Ising spins interact ferromagnetically with each other. Disorder is introduced by local random fields which act on each spin and whose values are drawn from a Gaussian distribution. At zero temperature, at a critical random-field strength h_c the system undergoes a phase transition.

Here, we consider an one-dimensional RFIM with long-range interactions that are only present between spins with a probability that decays like a power-law in the geometric distance between the interacting spins. The parameter σ in the power-law exponent enables us to tune the effective dimension of the model.

Different values of σ are used to investigate numerically [1] the three parameter regions, which are the mean-field, non-mean-field region and the region without a phase transition (h_c = 0). Ground states are calculated [2] with graph theoretical algorithms by mapping the system to a directed graph. The critical random-field strength h_c and the critical exponents are obtained by finite-size scaling and then compared to analytical predictions and to results of a hierarchical model [3].

[1] A.K. Hartmann: Practical Guide to Computer Simulations, World-Scientific, 2009
A. K. Hartmann and H. Rieger: Optimization Algorithms in Physics, Wiley-VCH, 2002
C. Monthus and T. Garel, J. Stat. Mech., P07010, 2011