Regensburg 2010 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 3: Complex energy landscapes (addendum to SYEL)

DY 3.3: Vortrag

Montag, 22. März 2010, 14:30–14:45, H42

Ground states of random-field Ising magnets around the upper critical dimension — •Björn Ahrens and Alexander K. Hartmann — University of Oldenburg

We consider the random-field Ising magnet (RFIM) around the upper critical dimension which is d_u=6. The RFIM consists of ferromagnetically coupled Ising spins with an additional quenched local random field. To ensure unique ground-states we choose Gaussian random fields with zero mean and a tuneable standard deviation h. When varying h, each realization of the disorder exhibits a rather complex energy landscape, in particular close to the ferromagnetic-paramegnetic phase transition. We obtain the ground state numerically [A.K. Hartmann, Practical Guide to Computer Simulations, World Scientific 2009]. For each realisation of disorder we map the random field to a graph with suitible chosen edge capacities [Picard and Ratliff, Networks 5, 357 (1975)]. For these graphs we calculate the maximum flow using a fast max-flow/min-cut algorithm, developed in algorithmic graph theory, which allows us to address large system sizes. Therein the minimum cut corresponds to a ground-state configuration of the system.

Using finite-size scaling, we obtain critical scaling exponents for correlation length, energy, magnetisation and susceptibility. The results for d=5 to d=7 are compared with the mean-field exponents of the RFIM, since from d_u=6 on the mean-field exponents are expected to hold.