Spontaneous magnetization probability distribution of a mean-field finite Ising model exhibiting a tricritical point

The mean field equilibrium magnetization distribution for a finite-size Ising model with pair and quartet interactions is used to monitor the first- and second-order phase transitions exhibited by this system. In the first-order transition region (triple point line) the magnetization distribution has three peaks of equal height, while in the second-order transition region (critical point line) this distribution shows a plateau. Triple and critical point lines meet at the tricritical point. A complete picture of the phase diagrm both for a finite-size lattice and at the thermodynamic limit is reported. An analysis of the fluctuations of the equilibrium magnetization per spin shows that they are O(N−1/2) for a paramagnetic or ferromagnetic equilibrium point, while they are O(N−1/4) for a critical point and O(N−1/6) for the tricritical point. Finite-size effects on the mean absolute value of the magnetization per spin and on the specific heat are also analyzed.