ИСТИНА

Starting from the archetypical geometrically frustrated magnetic objects - equilateral triangle and tetrahedron - we consider a multidimensional tetrahedron with spins 1/2 in the each vertex and equal antiferromagnetic Heisenberg exchange along each edge. Many-particle case is obtained by setting dimensionality d to high numbers, hence constitutung likely the most geometrically frustrated magnetic system ever possible. This problem has a remarkably easy exact solution for each d. As a result, this imaginary object demonstrates at d \to \infty all the features characteristic for the geometrically frustrated magnetic systems: a) highly degenerate ground state; b) absence of the magnetic phase transition down to T \to 0; c) perfect Curie-Weiss behavior well below Curie-Weiss temperature, down to T \to 0; d) vanishingly small exchange energy and magnetic entropy per one spin. Note that this system is not a subject of the Mermin-Wagner theorem, hence all these features are due solely to the geometrical frustration. We conclude that the system at might represents a quantum spin-liquid state. Therefore we present an exact solution of a quantum problem with Heisenberg exchange that, while bizarre, may nevertheless be considered as a quantum spin-liquid.