FIRST ORDER PHASE TRANSITIONS IN A SOLID WITH FINITE SIZE

First order phase transitions are rounded in solids of finite size. It is shown here that the above rounding is monitored by the correlation length ξL of the finite system, or equivalently by the so-called mass gap for the quantum Hamiltonian version of the model. Scaling with size is studied as a function of variable boundary conditions for the cylinder geometry (infinite strips with finite width), and a striking crossover is found in the mass gap behavior when the coupling g along the boundary becomes anti-periodic. For g>0, the rounding is exponential with size and an accurate determination of the spontaneous magnetization (order parameter) of the infinite system is obtained from numerical extrapolations.