Dresden 2011 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 42: Critical Phenomena and Phase Transitions
DY 42.1: Vortrag
Freitag, 18. März 2011, 10:15–10:30, ZEU 255
Ground states of random-field Ising magnets with correlated disorder — •Björn Ahrens and Alexander K. Hartmann — Universität Oldenburg
We consider the random-field Ising magnet (RFIM) in d=3 with correlated disorder. The RFIM consists of ferromagnetically coupled Ising spins with an additional quenched local random field. To ensure unique ground states the random field is chosen to be distributed according to a Gaussian with zero mean and a tunable standard deviation. Using Fourier transforms, we generate correlated random fields which exhibit a power-law shaped two-point correlation function. This well known method conserves the Gaussian distribution of the random field.
To obtain the ground state for each realisation of the disorder numerically, we map the random field to a graph with suitable chosen edge capacities [Picard and Ratliff, Networks 5, 357 (1975)]. For these graphs we calculate the maximum flow using a fast polynomial max-flow/min-cut algorithm, recently developed in algorithmic graph theory. Therein the minimum cut corresponds to a ground state configuration of the system. This allows to calculate exact ground states of systems up to N=1003 spins.
Similar to the RFIM with uncorrelated Gaussian disorder we find phase transitions for different two-point correlation functions. We obtain critical scaling exponents to analyse the transitions, using finite-size scaling.