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The article provides a tutorial review on how to treat Ising models withinmean-field (MF), effective-field (EF) and exact methods. MF solutions of thespin-1 Blume-Capel (BC) model and the mixed-spin Ising model demonstrate achange of continuous phase transitions to discontinuous ones at a tricriticalpoint. A quantum phase transition of the spin-S Ising model driven by atransverse field is explored within MF method. EF theory is elaborated within asingle- and two-spin cluster approach to demonstrate an efficiency of thisapproximate method. The long-standing problem of this method concerned with aself-consistent determination of the free energy is addressed. EF theory isadapted for the spin-1/2 Ising model, the spin-S BC model and the transverseIsing model. The particular attention is paid to continuous and discontinuoustransitions. Exact results for the spin-1/2 Ising chain, spin-1 BC chain andmixed-spin Ising chain are obtained using the transfer-matrix method, thecrucial steps of which are reviewed for a spin-1/2 Ising square lattice.Critical points of the spin-1/2 Ising model on several lattices are rigorouslyobtained with the help of dual, star-triangle and decoration-iterationtransformations. Mapping transformations are adapted to obtain exact resultsfor the mixed-spin Ising model on planar lattices. An increase in thecoordination number of the mixed-spin Ising model on decorated planar latticesgives rise to reentrant transitions, while the critical temperature of themixed-spin Ising model on a regular honeycomb lattice is always greater thanthat of two semi-regular archimedean lattices. The effect of selective sitedilution of the mixed-spin Ising model on a honeycomb lattice upon phasediagrams is examined. The review affords a brief account of the Ising modelssolved within MF, EF and exact methods along with a few comments on theirfuture applicability.

A brief account of the Ising and Ising-like models: Mean-field, effective-field and exact results