To simulate a first-order phase transition in an Ising model, we first implement, microscopically, a bias field where one of the spin states is energetically favoured over the other. We also implement degenerate states that are statistically favoured by constituents.
Recall the dice example from the Physics of Language (chapter four). A die has six distinct faces - or states. But now imagine that five of those faces have one dot on it while one face has six. Though the probability for each face to land face up, once thrown, is equal amongst them, the probability of a one being face up is five times more likely. In this case five faces of the die have equivalent states and as such are degenerate. A similar concept can be applied to spin states. Though the probabilities for individual states to occur are still the same, the fact that five states are effectively identical introduces a bias in favour of the identical states. The faces of a die are akin to the states of spins. However, spins can have an arbitrary number of states and an arbitrary number of these states may be equivalent or degenerate.
A competition between the bias field and the state of degeneracy is thus generated. On the one hand, the bias field is energetically favoured as it locks constituents in a low energy state through neighbour interaction, while on the other, degenerate states are statistically favoured. As energy is added to the system, local fluctuations in the state of constituents increase and influence the state of nearest neighbours. Degenerate states will be favoured despite the influence of the bias field. Constituents will hold on to their low energy states up to a critical point at which sufficient energy will be in the system that, statistically, constituents will tend to be in a degenerate state. This transition occurs suddenly.