Almeida-Thouless transition below six dimensions
Tam\'as Temesv\'ari
TL;DR
This paper demonstrates the existence of an Almeida-Thouless instability surface below six dimensions within a replica symmetric field theory, analyzing renormalization flows from mean field to lower dimensions.
Contribution
It shows the AT line persists below six dimensions by studying renormalization flows with temperature and magnetic field dependence in a replica symmetric framework.
Findings
AT instability surface exists below six dimensions
Renormalization flows reveal the fate of the AT line in lower dimensions
Analysis connects mean field results to finite-dimensional behavior
Abstract
The existence of an Almeida-Thouless (AT) instability surface below the upper critical dimension 6 is demonstrated in the generic replica symmetric field theory. Renormalization flows from around the zero-field fixed point are investigated. By introducing the temperature and magnetic field dependence of the bare parameters, the fate of the AT line can be followed from mean field (infinite dimensions) down to d<6.
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