Frustration - no frustration crossover and phase transitions in 2D spin models with zig-zag structure

Three 2D spin models made of frustrated zig-zag chains with competing interactions which by exact summation with respect to some degrees of freedom can be replaced by an effective temperature-dependent interaction were considered. The first model, exactly solvable Ising chains coupled by only four-spin interactions does not exhibit any finite temperature phase transition, nevertheless temperature can trigger a frustration - no frustration crossover accompanied by gigantic specific heat. A similar effect was observed in several two-leg ladder models [Yin Weiguo, arXiv:2006.08921v2 (2020), 2006.15087v1 (2020)]. The anisotropic Ising chains coupled by a direct interchain interaction and competing with it indirect interaction via spins located between chains are analyzed by using exact Onsager's equation and linear perturbation renormalization group (LPRG). Depending on the parameter set such a model exhibits one antiferromagnetic (AF) or ferromagnetic (FM) phase transition or three phase transitions with reentrant disordered phase between AF and FM ones. The LPRG method was also used to study coupled uniaxial $XXZ$ chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model for a certain set of parameters the model can undergo three phase transitions. However, both inchain and interchain plain interactions $s_{i,j}^x s_{k,l}^x+s_{i,j}^y s_{k,l}^y$ can eliminate the reentrant disordered phase and then only one transition takes place. Additionally, the $XXZ$ model can undergo temperature-induced metamagnetic transition.