Crossover anomalies in frustrated two-dimensional Ising spin system with four-spin interaction

As is well known, one-dimensional spin systems with short-range interactions cannot undergo a phase transition at finite temperature. However, in many 1D Ising spin models with frustration, at a certain crossover point, the thermodynamic quantities show anomalies that resemble such a transition W. Yin [Phys. Rev. Res. 6, 013331 (2024)]. Recently, Yin [Phys. Rev. Res. 6, 013331 (2024)] has shown, using decorated ladders as an example, that a one-dimensional Ising model can be arbitrarily close to the genuine phase transition. Using the transfer matrix method and real space renormalization group technique, we find that crossover resembling a phase transition accompanied by gigantic specific heat can also occur in two-dimensional systems. We consider coupled Ising spin chains with a zig-zag structure and a four-spin j(4) interaction, which allows us to control the temperature at which the spins become unbound in the model with short-range interactions. The crossover point is defined by two parameters: the crossover temperature t = t* and the crossover interaction j(4) = j(4)*, and occurs when the temperature at which the effective interaction between the spin subsystems zeros out coincides with the temperature at which the spins become unbound. In systems in which a genuine phase transition occurs at the critical temperature t = t(c), there are two possibilities: if t(c) > t* the system undergoes a sequence of three phase transitions with a reentrant transition to disordered phase, while for t(c) < t* the phase transition is preceded by the considered crossover. We study the key role in the appearance of anomalies in the thermodynamic quantities of the four-spin interactions which are suspected to have a significant impact on the properties of magnetic two-dimensional lattices, but possible also on the construction of social systems modeling the phenomenon of social validation or peer pressure.