Frustrated Spin Systems With First-Principles Approaches

In many antiferromagnetic spin systems, there are extensive configurations with competing energies, making it not possible to have one simple configuration satisfying all the interactions at the same time at low temperature. In those systems the magnetic order is strongly suppressed giving place to various exotic collective phenonmenon and phase transitions. This thesis studies some typical examples of novel phases and phase transitions in antiferromagnetic spin systems with first-principles approaches.First, the thesis studies the low-temperature physics of the SU(2)-symmetric spin-1/2 Heisenberg antiferromagnet on a pyrochlore lattice and find a fingerprint evidence for the thermal spin-ice state in this frustrated quantum magnet. Our conclusions are based on the results of bold diagrammatic Monte Carlo simulations, with good conver-gence of the skeleton series down to temperature T/J= 1/6. The identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for static structure factor between the quantum Heisenberg and classical Heisenberg/Ising models at all accessible temperatures, and the characteristic bow-tie pattern with pinch points observed at T/J= 1/6. The dynamic structure factor at real frequencies (obtained by analytic continuation of numerical data) is consistent with diffusive spinon dynamics at pinch points.The thesis also studies the 4-state Potts antiferromagnet and argues that the model has a finite-temperature phase transition on any Eulerian plane triangulation in which one’sublattice consists of vertices of degree 4. We furthermore predict the universality class of this transition. We then present transfer-matrix and Monte Carlo data confirm-ing these predictions for the cases of the union-jack and bisected hexagonal lattices. Futhermore. we exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antifer-romagnet has a finite-temperature phase transition at arbitrarily large values of q. The phase transition is called entropy-driven, since on the triangulation lattices one sublat-tice develops magnetic order so that other sublattices can have more degrees of freedom and therefore the entropy of the system gets increased. Additional numerical data are obtained using transfer matrices and Monte Carlo simulation.At last, the thesis studies the phase transitions in a particular infinite-coupling-limit of the Ashkin-Teller model and shows how the Hintermann-Merlini-Baxter-Wu model (which is a generalization of the well-known Baxter-Wu model to a general Eule-rian triangulation) can be mapped onto the infinite-coupling-limit of the Ashkin-Teller model. We work out some mappings among these models, also including the stan- dard and mixed Ashkin-Teller models. Finally, we compute the phase diagram of the infinite-coupling-limit Ashkin-Teller model on the square, triangular, hexagonal, and kagome lattices.