Supersymmetric statistical models on the lattice

SUSY models in statistical mechanics involve spinless fermions and form an ideal laboratory for latticization. Extension of SUSY relations to the lattice may clarify, as well, the question of their validity beyond perturbation theory. A non-linear approach to lattice SUSY is introduced by the assignment of coupled commuting and anticommuting variables to each lattice site. As a typical example we demonstrate a SUSY dimer Hamiltonian which generates lattice branched-polymers configurations. We suggest a new SUSY model whose configurations are generated by the Ising super-Hamiltonian. These configurations cannot be simply related to the high temperature expansion of the random-field Ising model. The critical behavior of the random-field model is probably in the non-perturbative regime with thermal fluctuations squeezed into anti d-dimensional manifolds in the boundaries of frozen domains. Self-consistent dimensional reduction yields anti d = (d + 1/nu)/2 if ..cap alpha.. < 0 and anti d = d - 1/nu if ..cap alpha.. > 0. This may be explained in terms of anomalous anticommuting dimensions. 18 references