2015/04/21 by А. В. Андрианов, Andrianov, A. Vl.
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Physics and Astronomy · #FOS: Physical sciences #Geomagnetism and Paleomagnetism Studies #Geophysics and Gravity Measurements #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1504.05622
openalex publication_date 2015/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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→∞ 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→0; and vanishingly small exchange energy per one spin.