Renormalization group for the probability distribution of magnetic impurities in a random-field $\phi^4$ model

TL;DR

This paper develops a renormalization group approach for the probability distribution of magnetic impurities in a random-field $^4$ model, highlighting effects beyond the upper critical dimension.

Contribution

It introduces new parameters for the probability distribution of impurities and explores their impact on critical phenomena in lower dimensions.

Findings

New parameters influence critical behavior below the upper critical dimension

Dimensional reduction is reconsidered with the extended RG approach

Impurities' probability distribution affects phase transition properties

Abstract

Extending the usual Ginzburg-Landau theory for the random-field Ising model, the possibility of dimensional reduction is reconsidered. A renormalization group for the probability distribution of magnetic impurities is applied. New parameters corresponding to the extra $\phi^4$ coupling constants in the replica Hamiltonian are introduced. Although they do not affect the critical phenomena near the upper critical dimension, they can when dimensions are lowered.