Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems (Q2872266)

The authors consider Ising spin systems, defined on a finite set of sites, decomposable to subsystems called units with the property that each site belongs to either one or two units such as Kagome lattice, Checkerboard and ladder. It should be mentioned that the internal energy of the system is assumed to be the sum of the internal energy of the units which are assumed to be symmetric in the spins of the unit. The authors show in Section 3 that under certain conditions on the interactions among the spins, the Lee-Yang zeros of the partition function by which the thermodynamic properties of the system are determined, are bounded away from the positive real z axis at low temperature or, under stronger conditions, the zeros must lie on the negative real axis. Indeed, the authors' obtained models, after suitable rescaling, include the monomer-dimer model and the graph-counting models of \textit{D. Ruelle} [J. Algebr. Comb. 9, No. 2, 157--160 (1999; Zbl 0915.05068); Commun. Math. Phys. 200, No. 1, 43--56 (1999; Zbl 0917.05074)]. Thus, it is interesting to mention that the authors successfully generalize the well-known and important result of \textit{O. J. Heilmann} and \textit{E. H. Lieb} [Commun. Math. Phys. 25, 190--232 (1972; Zbl 0228.05131); erratum ibid. 27, No. 166 (1972)] that the Lee-Yang zeros of monomer-dimer systems are real and negative.