Pseudo-critical behavior of spin-1/2 Ising diamond and tetrahedral chains

Abstract

A few paradigmatic one-dimensional lattice-statistical spin models have recently attracted a vigorous scientific interest owing to their peculiar thermodynamic behavior, which is highly reminiscent of a temperature-driven phase transition. The pseudotransitions of one-dimensional lattice-statistical spin models differ from actual phase transitions in several important aspects: the first-order derivatives of the Gibbs free energy such as entropy or magnetization exhibit near a pseudo-transition an abrupt continuous change instead of a true discontinuity, whereas the second-order derivatives of the Gibbs free energy such as specific heat or susceptibility display near a pseudo-transition a vigorous finite peak instead of an actual power-law divergence. In the present chapter we will comprehensively examine a pseudo-critical behavior of the spin-1/2 Ising diamond and tetrahedral chains by a detailed examination of basic magnetothermodynamic quantities such as the entropy, specific heat and susceptibility. It will be demonstrated that density plots of these magnetothermodynamic quantities provide a useful tool for establishing a finite-temperature diagram, which clearly delimits boundaries between individual quasi-phases in spite of a lack of true spontaneous long-range order at any nonzero temperature. It is suggested that a substantial difference between the degeneracies of two ground states of the spin-1/2 Ising diamond and tetrahedral chains is an essential prerequisite for observation of a relevant pseudo-critical behavior in a close vicinity of their ground-state phase boundary.

18 pages, 11 figures, book chapter to "An Introduction to the Ising model" to be published by Nova Science Publisher

References in corpus (6)

• Geometric frustration in the class of exactly solvable Ising-Heisenberg diamond chains
• Vigorous thermal excitations in a double-tetrahedral chain of localized Ising spins and mobile electrons mimic a temperature-driven first-order phase transition
• Quasi-phases and pseudo-transitions in one-dimensional models with nearest neighbor interactions
• Thermal entanglement and sharp specific-heat peak in an exactly solved spin-1/2 Ising-Heisenberg ladder with alternating Ising and Heisenberg inter-leg couplings
• Peculiarities in pseudo-transitions of a mixed spin-$(1/2,1)$ Ising-Heisenberg double-tetrahedral chain in an external magnetic field
• Interplay between spin frustration and thermal entanglement in the exactly solved Ising-Heisenberg tetrahedral chain

Cited by in corpus (2)

• Bifurcation in correlation length of the Ising model on a "Toblerone" lattice
• Finding and classifying an infinite number of cases of the marginal phase transition in one-dimensional Ising models