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A variational study of the random-field XY model

T. Garel·G. Iori·H. Orland
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Abstract

A disorder-dependent Gaussian variational approach is applied to the $d$-dimensional ferromagnetic XY model in a random field. The randomness yields a non extensive contribution to the variational free energy, implying a random mass term in correlation functions. The Imry-Ma low temperature result, concerning the existence ($d>4$) or absence ($d < 4$) of long-range order is obtained in a transparent way. The physical picture which emerges below $d=4$ is that of a marginally stable mixture of domains. We also calculate within this variational scheme, disorder dependent correlation functions, as well as the probability distribution of the Imry-Ma domain size.

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T. Garel, G. Iori, H. Orland. 1995-12-08. A variational study of the random-field XY model. https://doi.org/10.1103/physrevb.53.r2941

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