Is order-by-disorder present or absent in a highly frustrated region of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices?

TL;DR

This paper provides an exact solution for the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices, revealing conditions under which order-by-disorder phenomena occur or are absent in highly frustrated regions.

Contribution

It introduces an exact analytical approach combining star-triangle transformation and recursion relations to analyze frustration and order-by-disorder in this model.

Findings

Highly frustrated regions show quantum disorder at all temperatures.

Higher connectivity in the lattice induces quantum order at low temperatures.

Magnetizations decrease with increasing lattice coordination number.

Abstract

The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three inter-connected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes with increasing the coordination number of underlying Husimi lattice.