Journal of Physical Studies 5(3/4), 285–292 (2001)
DOI: https://doi.org/10.30970/jps.05.285

CRITICAL BEHAVIOUR OF WEAKLY DISORDERED SYSTEMS WITH REPLICA SYMMETRY BREAKING POTENTIALS

P. V. Prudnikov, V. V. Prudnikov

Department of Theoretical Physics, Omsk State University
55a, Pr. Mira, Omsk, 644077, Russia

A field-theoretic description of the critical behaviour of the weakly disordered systems is given. Directly, for three- and two-dimensional systems a renormalization analysis of the effective Hamiltonian of the model with replica symmetry breaking (RSB) potentials is carried out in the two-loop approximation. For the case with first-step RSB the fixed points (FPs) corresponding to the stability of the various types of critical behaviour are identified with the use of the Padé-Borel summation technique. The analysis of FPs has shown a stability of the critical behaviour of the weakly disordered three- and two-dimensional systems with respect to RSB effects and realization of the former scenario of disorder influence on critical behaviour. For the case of systems with arbitrary dimension from 3 to 4 the ranges of critical behaviour determined by the RSB effects are found for each value of the $p$-component order parameter without the use of $ε$-expansion. A comparison with the results of the $ε$-expansion calculations is carried out.

PACS number(s): 64.60.Ak, 64.60.Fr, 64.60.Ht

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