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Physical review. B, Condensed matter

Real-space renormalization-group study of random-superconductor models

Michel J. P. Gingras

Published Jun 1, 1991• 18 citations
Publisher

Abstract

A zero-temperature Migdal-Kadanoff renormalization-group scheme is used to investigate two classical spin-glass lattice models of a random superconductor in a magnetic field. We show that the two models considered here become the same under renormalization and belong to a different universality class from the Ising and XY spin glasses. We find that, in contrast with results from recent Monte Carlo simulations, the lower critical dimension for a nonzero-temperature vortex-glass transition in a random superconductor is greater than 3.

DOI
10.1103/physrevb.43.13747

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A zero-temperature Migdal-Kadanoff renormalization-group scheme is used to investigate two classical spin-glass lattice models of a random superconductor in a magnetic field. We show that the two models considered here become the same under renormalization and belong to a different universality class from the Ising and XY spin glasses. We find that, in contrast with results from recent Monte Carlo simulations, the lower critical dimension for a nonzero-temperature vortex-glass transition in a random superconductor is greater than 3.
Here is the first part of the summary of my work on random Ising model using real-space renormalization group (RSRG), also known as a Migdal-Kadanoff one. This approximate renormalization scheme was applied to the analysis thermodynamic properties of the model, and of probabilistic properties of a pair correlator, which is a fluctuating object in disordered systems. PACS numbers: 02.50.-r, 05.20.-y, 05.70.Fh, 64.60.ae, 75.10.-b, 75.10.Hk, 87.10.+e Keywords: statistical physics, magnetism, spin glass, neural networks
The random-field XY model is studied in spatial dimensions d=3 and 4, and in between, as the limit q→∞ of the q-state clock models, by the exact renormalization-group solution of the hierarchical lattice or, equivalently, the Migdal-Kadanoff approximation to the hypercubic lattices. The lower critical dimension is determined between 3.81<d_{c}<4. When the random field is scaled with q, a line segment of zero-temperature criticality is found in d=3. When the random field is scaled with q^{2}, a universal phase diagram is found at intermediate temperatures in d=3.