  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.
