Year: 2015
Type: preprint
Abstract: Starting from the archetypical geometrically frustrated magnetic objects -- equilateral triangle and tetrahedron -- we consider an imaginary object: a multidimensional tetrahedron with spins $1/2$ in the each vertex and equal Heisenberg magnetic exchange along each edge. Many-particle case is obtained by setting dimensionality $d$ to high numbers, hence providing likely the most geometrically frustrated magnetic system ever possible. This problem has an exact solution for each $d$, obtained by simple student-level approach. As a result, this imaginary object clearly demonstrates at $d\to{}\infty$ all the features characteristic for the real geometrically frustrated magnetic systems: highly-degenerate ground state; absence of the magnetic phase transition; perfect Curie-Weiss behavior down to $T\to{}0$; and vanishingly small exchange energy per one spin.
Source: arXiv (Cornell University)
Author: Andrianov, A. Vl.
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W776582344