I was simulating the square lattice Ising model via Metropolis Algorithm and found that at 0 magnetic field, there is spontaneous magnetisation below some temperature.
I have used Periodic Boundary Condition in a 100x100 lattice. Is this an instance of a Phase Transition? I have heard that phase transitions occur in thermodynamic limit. So how does this spontaneous magnetisation occur?
If this is not a phase transition, is it an artifice of the metropolis algorithm and relates to non convergence of this algorithm?
If this is a phase transition how does spontaneous magnetisation occur at all since the probabilities carry the symmetry of the hamiltonian and the partition function is finite allowing the microstates to have boltzmann distribution for all magnetisation values?