Collège Doctoral - Doktorandenkollegien

Statistical Physics of Complex Systems

Coventry - Leipzig - Lviv - Nancy

PhD positions


Title Hyperscaling above the upper critical dimension
Authors Berche B., Kenna R., Walter J.C.
Reference Nucl. Phys. B 865 [FS] (2012) 115-132
Abstract Above the upper critical dimension, the breakdown of hyperscaling is associ- ated with dangerous irrelevant variables in the renormalization group formalism at least for systems with periodic boundary conditions. While these have been exten- sively studied, there have been only a few analyses of finite-size scaling with free boundary conditions. The conventional expectation there is that, in contrast to periodic geometries, finite-size scaling is Gaussian, governed by a correlation length comensurate with the lattice extent. Here, detailed numerical studies of the five- dimensional Ising model indicate that this expectation is unsupported, both at the infinite-volume critical point and at the pseudocritical point where the finite-size susceptibility peaks. Instead the evidence indicates that finite-size scaling at the pseudocritical point is similar to that in the periodic case. An analytic explana- tion is offered which allows hyperscaling to be extended beyond the upper critical dimension.

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