An open question in the study of the spin-1/2 Ising model is the solution of the two-dimensional case in the presence of a magnetic field. A possible answer is based on the study of L-coupled linear chains in the limit of large L. Results reported in the literature show that a dimensional crossover from the one to the two dimensional model does not exist. However, what happens if one considers open boundary conditions (BC)? In this article I show that, for an appropriate choice of the BC, a system of L-chains exhibits a ferromagnetic order characterized by a critical temperature which, for zero magnetic field, tends to the Onsager's one as L increases. It is then possible to study the phase diagram in the (h, T) plane and obtain a solution for finite magnetic field.
Phase transitions in Ising Chains?
MANCINI, Ferdinando
2009
Abstract
An open question in the study of the spin-1/2 Ising model is the solution of the two-dimensional case in the presence of a magnetic field. A possible answer is based on the study of L-coupled linear chains in the limit of large L. Results reported in the literature show that a dimensional crossover from the one to the two dimensional model does not exist. However, what happens if one considers open boundary conditions (BC)? In this article I show that, for an appropriate choice of the BC, a system of L-chains exhibits a ferromagnetic order characterized by a critical temperature which, for zero magnetic field, tends to the Onsager's one as L increases. It is then possible to study the phase diagram in the (h, T) plane and obtain a solution for finite magnetic field.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
