Fluctuation interaction of Ising subsystems

A phase diagram of two Ising subsystems $\sigma$ and $s$ has been constructed on a Bethe lattice with a coordination number 4 (a simplified analog of a square lattice). In contrast to the known Ashkin-Teller model, the interaction between these two subsystems is of a purely fluctuational nature; i.e., it does not manifest itself in the ground state and nullifies the sums of the products of average spins $\langle\sigma \rangle\langle s\rangle$ (interactions of this type are realized in lattice-type adsorbed systems with dipolelike intermolecular interactions and strong azimuthal angular dependence of the adsorption potential of symmetry C$_4$). Apart from conventional states, i.e., a high-temperature disordered state ($\langle\sigma \rangle=\langle s\rangle=0$) and a low-temperature ordered state ($\langle\sigma \rangle$ и $\langle s\rangle \neq 0$), this system can also exist in a correlated state ($\langle\sigma s\rangle\neq 0$ at $\langle\sigma \rangle=\langle s\rangle=0$). In the theory of orientational phase transitions, this state corresponds to a fundamentally different, intermediate (on the temperature axis) phase in which a preferred direction of long molecule axes arises in the absence of spontaneous polarization. The results of Monte Carlo simulation on a square lattice agree with the conclusions obtained on a Bethe lattice. The characteristics of the orientational phase transition in a $2\times1$ monolayer of CO molecules adsorbed on the NaCl(100) surface are discussed.