Dresden 2009 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 6: Critical phenomena and phase transitions
DY 6.2: Vortrag
Montag, 23. März 2009, 15:00–15:15, ZEU 118
Exact ground states in 6d random-field Ising magnets — •Björn Ahrens and Alexander Karl Hartmann — Universität Oldenburg, Germany
We calculate exact ground states of random-field Ising magnets (RFIM) in 6 dimensions up to lattice sizes of L=10. We calculate some critical exponents and compare them with previously obtained mean-field exponents.
The RFIM is a disordered system. It consists of ferromagnetically coupled Ising spins with an additional quenched local magnetic field. Here the field is Gaussian distributed with a fixed mean =0 and a tuneable standard deviation.
To obtain a ground state of a realisation of the disorder we map the random field to a graph with suitible chosen edge capacities [Picard and Ratliff, 1975]. For these graphs we calculate the maximum flow using a fast max-flow/min-cut algorithm, recently developed in algorithmic graph theory. The minimum cut corresponds to a ground state configuration of the system. We can measure the bond energy, the magnetisation and the susceptibility by applying a small extern field . Using finite-size scaling we can calculate t he specific heat exponent α, the order parameter exponent β, the susceptibility exponent γ and the correlation length exponent ν. They are compared with the mean-field exponents of the RFIM, because du≤ 6 is the upper critical dimension [Tasaki, 1989] from which on the mean-field exponents should hold.