FINITE-SIZE SCALING OF THE MASS-GAP FOR 1ST-ORDER PHASE-TRANSITIONS

I summarize recent work on finite-size scaling in long cylinders, partially obtained in collaboration with J. Imbrie. It is sketched how a system in a long cylinder can be mapped onto a one dimension spin system. For the low temperature Ising model, one obtains the finite-size scaling of the mass-gap as a function of the cross-section A = L(d-1) and the magnetic field h. I discuss a recent controversy stemming from the numerical work of Shen and Jansen on the finite-size scaling of this mass-gap for d = 4 and h = 0, and argue that the observed discrepancy is a crossover effect. In a second part, I consider the q states Potts model. I discuss both the finite-size scaling of the mass-gap in long cylinders and the numerical determination of the interface tension. I present an exact formula for the interface tension in d = 2 which has been recently obtained by W. Janke and myself.