We consider the thermal phase transition from a paramagnetic to stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J1 < 0 (nearest neighbor, ferromagnetic) and J2 > 0 (second neighbor, antiferromagnetic). The striped phase breaks a Z4 symmetry and is stabilized at low temperatures for g = J2/|J1| > 1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [PRL 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The J1-J2 model has a line of very weak first-order phase transitions in the whole region 1/2 < g < g * , where g * = 0.67 ± 0.01. Thereafter, the transitions from g = g * to g → ∞ are continuous and can be fully mapped, using universality arguments, to the critical line of the well known Ashkin-Teller model from its 4-state Potts point to the decoupled Ising limit. We also comment on the pseudo-first-order behavior at the Potts point and its neighborhood in the AshkinTeller model on finite lattices, which in turn leads to the appearance of similar effects in the vicinity of the multicritical point g * in the J1-J2 model. The continuous transitions near g * can therefore be mistaken to be first-order transitions, and this realization was the key to understanding the paramagnetic-striped transition for the full range of g > 1/2. Most of our results are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological bench-marks for weakly first-order behaviors and Ashkin-Teller criticality.

We study the challenging thermal phase transition to stripe order in the frustrated square-lattice Ising model with couplings J(1) < 0 (nearest-neighbor, ferromagnetic) and J(2) > 0 (second-neighbor, antiferromagnetic) for g = J(2)/|J(1| > 1/2. Using Monte Carlo simulations and known analytical results, we demonstrate Ashkin-Teller criticality for g ≥ g*; i.e., the critical exponents vary continuously between those of the 4-state Potts model at g = g* and the Ising model for g → ∞. Thus, stripe transitions offer a route to realizing a related class of conformal field theories with conformal charge c = 1 and varying exponents. The transition is first order for g < g* = 0.67 ± 0.01, much lower than previously believed, and exhibits pseudo-first-order behavior for |g* ≤ g

We study three-dimensional dimerized S = 1/2 Heisenberg antiferromagnets, using quantum Monte Carlo simulations of systems with three different dimerization patterns. We propose a way to relate the Néel temperature TN to the staggered moment ms of the ground state. Mean-field arguments suggest TN ∝ ms close to a quantum-critical point. We find an almost perfect universality (including the prefactor) if TN is normalized by a proper lattice-scale energy. We show that the temperature T * at which the magnetic susceptibility has a maximum is a good choise, i.e., TN /T * versus ms is a universal function (also beyond the linear regime). These results are useful for analyzing experiments on systems where the spin couplings are not known precisely, e.g., TlCuCl3.

We study the S=1/2 Heisenberg (J) model on the two-dimensional square lattice in the presence of additional higher-order spin interactions (Q) which lead to a valence-bond-solid (VBS) ground state. Using quantum Monte Carlo simulations, we analyze the thermal VBS transition. We find continuously varying exponents, with the correlation-length exponent "nu" close to the Ising value for large Q/J and diverging when Q/J approaches the quantum-critical point (the critical temperature Tc -> 0). This is in accord with the theory of deconfined quantum-critical points, which predicts that the transition should approach a Kosterlitz-Thouless (KT) fixed point when Tc -> 0+ (while the transition versus Q/J for T=0 is in a different class). We find explicit evidence for KT physics by studying the emergence of U(1) symmetry of the order parameter at T=T_c when Tc -> 0.Comment: 5 pages, 5 figure