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Continuous approach for the random-field Ising chain

  • We study the random-field Ising chain in the limit of strong exchange coupling. In order to calculate the free energy we apply a continuous Langevin-type approach. This continuous model can be solved exactly, whereupon we are able to locate the crossover between an exponential and a power-law decay of the free energy with increasing coupling strength. In terms of magnetization, this crossover restricts the validity of the linear scaling. The known analytical results for the free energy are recovered in the corresponding limits. The outcomes of numerical computations for the free energy are presented, which confirm the results of the continuous approach. We also discuss the validity of the replica method which we then utilize to investigate the sample-to-sample fluctuations of the finite size free energy

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Author:Rüdiger Zillmer, Arkady S. PikovskyORCiDGND
Document Type:Article
Year of first Publication:2005
Year of Completion:2005
Release Date:2017/03/24
Source:Physical Review / e. - 72 (2005), 5, S. 7
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert
Institution name at the time of publication:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik