Fermion Correlation Functions in the Disordered Quantum Ising Model

Antoine Georges, David Hansel, Pierre Le Doussal +1 more

The exact calculation of an infinite number of correlation functions for general cubic and HCP anisotropic Ising models on their 'disorder variety' is described. The intra-plane correlation functions are found to be exactly the same as for a two-dimensional free-fermion Ising model. This allows the authors to characterise the intersection between the disorder and critical variety which displays in general anisotropic scaling with non-trivial exponents.

Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu

J. Rae

Ferenc Iglói, István A. Kovács

The critical behavior of the random transverse-field Ising model in finite-dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder renormalization-group (SDRG) method. Here we extend these studies and calculate the connected transverse-spin correlation function by a numerical implementation of the SDRG method in $d=1,2$, and 3 dimensions. At the critical point an algebraic decay of the form $\ensuremath{\sim}{r}^{\ensuremath{-}{\ensuremath{\eta}}_{t}}$ is found, with a decay exponent being approximately ${\ensuremath{\eta}}_{t}\ensuremath{\approx}2+2d$. In $d=1$ the results are related to dimer-dimer correlations in the random antiferromagnetic $XX$ chain and have been tested by numerical calculations using free-fermionic techniques.

Charles M. Newman, Michael Aizenman, Abel Klein

Bershadskii-breve, I.D. Vai-brevesburd, Alexander Migdal

We have constructed a Majorana fermion representation of the two-dimensional Ising model on an irregular triangulated lattice with the topology of a sphere and of a torus and also a fermion representation of the correlation function of disorder operators on the dual lattice. The representations obtained give the possibility of a nonperturbative analysis of the fermion string and in particular, may be used for Monte Carlo simulation.