About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Paper
Phase transitions and tricritical points: An exactly soluble model for magnetic or distortive systems
Abstract
We present and solve exactly a lattice model for magnetic or for structural phase transitions. The model proposed here can be seen as an extension of the spherical model. We obtain the following results: (i) The free energy of the system is calculated rigorously in a general case for lattices of any dimensionality d or structure. (ii) The critical properties are worked out explicitly for a special case of the interaction on a cubic d-dimensional lattice (d may be a fractional number). If d>2, second-order phase transitions may occur. The critical exponents are those of the sperical model. (iii) For a special choice of the interaction and if d3, the existence of a line of tricritical points can be demonstrated. The tricritical exponents are computed explicitly; they are identical to the exponents of the "Gaussian" model. (iv) Finally, first-order phase transitions are shown to exist in one and two dimensions. © 1977 The American Physical Society.