Monte Carlo Renormalization Group for Classical Lattice Models with Quenched Disorder

Yantao Wu, Roberto Car

Research output: Contribution to journalArticlepeer-review

Abstract

We extend to quenched-disordered systems the variational scheme for real-space renormalization group calculations that we recently introduced for homogeneous spin Hamiltonians. When disorder is present our approach gives access to the flow of the renormalized Hamiltonian distribution, from which one can compute the critical exponents if the correlations of the renormalized couplings retain finite range. Key to the variational approach is the bias potential found by minimizing a convex functional in statistical mechanics. This potential reduces dramatically the Monte Carlo relaxation time in large disordered systems. We demonstrate the method with applications to the two-dimensional dilute Ising model, the random transverse field quantum Ising chain, and the random field Ising in two- and three-dimensional lattices.

Original languageEnglish (US)
Article number190601
JournalPhysical review letters
Volume125
Issue number19
DOIs
StatePublished - Nov 3 2020

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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