Numerical Replica Limit for the Density Correlation of the Random Dirac Fermion

Details Numerical Replica Limit for the Density Correlation of the Random Dirac Fermion Numerical Replica Limit for the Density Correlation of the Random Dirac Fermion

2000-12-13

arxiv.org/abs/cond-mat/0012218v1

Phys. Rev. B 63, 233307 (2001)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 4 figures, REVTeX

Scientific paper

10.1103/PhysRevB.63.233307

The zero mode wave function of a massless Dirac fermion in the presence of a random gauge field is studied. The density correlation function is calculated numerically and found to exhibit power law in the weak randomness with the disorder dependent exponent. It deviates from the power law and the disorder dependence becomes frozen in the strong randomness. A classical statistical system is employed through the replica trick to interpret the results and the direct evaluation of the replica limit is demonstrated numerically. The analytic expression of the correlation function and the free energy are also discussed with the replica symmetry breaking and the Liouville field theory.

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