Abstract. We restudy the phase diagram of the 2D-Ising model with competing interactions J1 on nearest neighbour and J2 on next-nearest neighbour bonds via Monte-Carlo simulations. We present the finite temperature phase diagram and introduce computational methods which allow us to calculate transition temperatures close to the critical point at J2 = J1/2. Further on we investigate the character of the different phase boundaries and find that the transition is weakly first order for moderate J2 > J1/2.

We analyze the phase transition of the frustrated J1-J2 Ising model with antiferromagnetic nearestand strong next-nearest neighbor interactions on the square lattice. Using extensive Monte Carlo simulations we show that the nature of the phase transition for 1/2 < J2/J1 1 is not of the weakly universal type -as commonly believed -but we conclude from the clearly doubly peaked structure of the energy histograms that the transition is of weak first order. Motivated by these results, we analyze the phase transitions via field-theoretic methods; i.e., we calculate the central charge of the underlying field theory via transfer-matrix techniques and present, furthermore, a field-theoretic discussion on the phase-transition behavior of the model. Starting from the conformally invariant fixed point of two decoupled critical Ising models (J1 = 0), we calculate the effect of the nearest neighbor coupling term perturbatively using operator product expansions. As an effective action we obtain the Ashkin-Teller model.

We use improved Monte-Carlo algorithms to study the antiferromagnetic 2D-Ising model with competing interactions J1 on nearest neighbour and J2 on next-nearest neighbour bonds. The finite-temperature phase diagram is divided by a critical point at J2 = J1/2 where the groundstate is highly degenerate. To analyse the phase boundaries we look at the specific heat and the energy distribution for various ratios of J2/J1. We find a first order transition for small J2 > J1/2 and the transition temperature suppressed to TC = 0 at the critical point. Neel orderCollinear order NN NNN bonds

We report on Monte Carlo simulations for the two-dimensional frustrated J1-J2 Ising model on the square lattice. Recent analysis has shown that for the phase transition from the paramagnetic state to the antiferromagnetic collinear state different phase-transition scenarios apply depending on the value of the frustration J2/J1. In particular a region with critical Ashkin-Teller-like behavior, i.e., a second-order phase transition with varying critical exponents, and a noncritical region with first-order indications were verified. However, the exact transition point [J2/J1]C between both scenarios was under debate. In this paper we present Monte Carlo data which strengthens the conclusion of Jin et al. [Phys. Rev. Lett. 108, 045702 (2012)] that the transition point is at a value of J2/J1 ≈ 0.67 and that double-peak structures in the energy histograms for larger values of J2/J1 are unstable in a scaling analysis.

We investigate the phase diagram of hard-core bosons on a square lattice with competing interactions. The hard-core bosons can also be represented by spin-1/2 operators and the model can therefore be mapped onto an anisotropic J1-J2-Heisenberg model. We find the Néel state and a collinear antiferromagnetic state as classical ordered phases to be suppressed by the introduction of ferromagnetic exchange terms in the x-y plane which result in a ferromagnetic phase for large interactions. For an intermediate regime, the emergence of new quantum states like valence bond crystals or super-solids is predicted for similar models. We do not observe any signal for long-range order in terms of conventional order or dimer correlations in our model and find an exponential decay in the spin correlations. Hence, all evidence is pointing towards a quantum-disordered ground state for a small region in the phase diagram. PACS numbers: quantum spin frustration, 75.10.Jm; Magnetic phase transitions, 75.30.Kz; computer modeling and simulation 75.40.Mg