“…Mostly they have been models in two and three dimensions. For instance, in several works on High Temperature Superconductivity the transition from paramagnetic (PM) to non-pure FM ordered phases has been studied [1,2,3,4]. On the other hand, in relation to the finite temperature phase transition in pure gauge SU(3), the d = 3 three state Potts model with negative second neighbour couplings was unsuccessfully considered to find a new critical behaviour [5,6].…”
We study the phase diagram of the four dimensional Ising model with first and second neighbour couplings, specially in the antiferromagnetic region, by using Mean Field and Monte Carlo methods. From the later, all the transition lines seem to be first order except that between ferromagnetic and disordered phases in a region including the first-neighbour Ising transition point.
“…Mostly they have been models in two and three dimensions. For instance, in several works on High Temperature Superconductivity the transition from paramagnetic (PM) to non-pure FM ordered phases has been studied [1,2,3,4]. On the other hand, in relation to the finite temperature phase transition in pure gauge SU(3), the d = 3 three state Potts model with negative second neighbour couplings was unsuccessfully considered to find a new critical behaviour [5,6].…”
We study the phase diagram of the four dimensional Ising model with first and second neighbour couplings, specially in the antiferromagnetic region, by using Mean Field and Monte Carlo methods. From the later, all the transition lines seem to be first order except that between ferromagnetic and disordered phases in a region including the first-neighbour Ising transition point.
The spiral state in the two-dimensional t-J model is studied by numerical diagonalization of an effective Hamiltonian. We examine all possibilities of the spiral spin states including the nonplanar states. It is found that nonplanar spiral states occur, but the deviations from the planar spiral state in the nonplanar spiral states are small for small hole concentrations where our effective Hamiltonian is valid. The modulation of the spin configuration increases continuously from the antiferromagnetic order as the hole concentration increases, and discontinuously changes at a critical hole concentration. Then the state undergoes the first-order phase transition either to the (s, O) phase or to the ferromagnetic phase, depending on the value of J/t
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