The onset of two-dimensional tricritical behavior in $N\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$ strips of spins in an Ising-like model is investigated. This is done through numerical computation of the largest eigenvalue of the single-spin advance transfer matrix. Primary attention is paid to the specific heat at constant nonordering field. The usual phase diagram, in zero ordering field, locates the tricritical point at the intersection of a first-order line and a $\ensuremath{\lambda}$ line; it is found here that a curve of large-field, rounded and bounded specific-heat peaks also seems to intersect this point. This curve, when it exists, may be helpful in experimentally locating tricritical points in any dimension. Evidence is also presented, at zero nonordering field, for the validity of the Onsager specific-heat temperature shift ${N}^{\ensuremath{-}2}\mathrm{ln}N$ in the model.
The tricritical behavior of a classical three-well-potential model for two-component systems (such as
He3-
He4 mixtures) is discussed by using renormalization-group techniques. The tricritical exponents and scaling fields are calculated for three dimensions.
By using Kadanoff's variational renormalization-group method an Ising model with vacancies is investigated for dimensions up to
d=4 to study the crossover to classical behavior. Up to a crossover dimension $d\ensuremath{\simeq}3.4$, both an optimal critical and tricritical fixed point are located with critical indices that agree well with other data. At $d\ensuremath{\simeq}3.4$, both fixed points merge, representing in this way the crossover to classical behavior. At
d>3.4, indications are found that the two fixed points do not annihilate but form a "marginal" pair that describes both critical and tricritical behavior.