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Physica A Statistical Mechanics and its Applications

Random field effects in a Bose system: Critical behaviour and crossover phenomena in the Hartree limit

Gaetano Busiello, L. De Cesare, Ileana Rabuffo

Published Jun 1, 1984• 9 citations
Publisher
DOI
10.1016/0378-4371(84)90151-1

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Abstract The effect of quenched random fields on the zero‐temperature critical behaviour is studied by the means of the Wilson‐Fisher renormalisation‐group recursion relations to first order in the ϵ‐expansion. A number of quantum models is considered. The simultaneous influence of both, the random‐field and the classical‐to‐quantum dimensional crossover phenomena on the quantum critical behaviour is investigated. A special attention is paid to the properties of some reasonable particular forms of Gaussian random correlations which might be of relevance to the description of natural systems.
The scaling theory of finite size effects in the limiting bulk behaviour is extended to treat crossover phenomena. The method is used to study quantum critical phenomena in the XY chain in a transverse field at zero temperature, through the scaling of the longitudinal susceptibilities and of the energy gaps between the ground and two first excited states. As expected, no abrupt change in critical exponents is observed for small anisotropy. Because of the finiteness of the system, but the limiting isotropic and anisotropic regions display quite distinct critical behaviour, in good agreement with known results. Another interesting result obtained is that the two energy gaps examined vanish at the critical line with the same critical exponent.