QUANTUM HEISENBERG FERROMAGNETS AND STOCHASTIC EXCLUSION PROCESSES

Let H be the isotropic spin-s quantum ferromagnetic Heisenberg Hamiltonian associated with a finite volume in ℤd. In an appropriate representation, the restriction of - H to the N-spin wave sector - HN can be regarded as the generator of a Markov semigroup exp( - tHN). For s = 1/2 the corresponding process XN (t) is identified as a simple N-particle exclusion process; for higher spin it is a more complicated exclusion process involving different species of particles. A Feynman-Kac, Cameron-Martin perturbation formula for exp( - tHN) is developed in the s = 1/2 case, and the formula is used to obtain some thermodynamic correlation inequalities. © 1980 American Institute of Physics.