Analysis of the phase transition for the Ising model on the frustrated square lattice

Abstract

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.

Phase transitions in a frustrated Ising antiferromagnet on a square lattice

“…c -0 .5 . Such behavior is confirmed not only by approximate methods [8,9,12], but also by recent Monte Carlo studies [13][14][15]28]. We note that the region of -1.1 < R < -0 .6 7 turns out to be very difficult to study by numerical means; nevertheless, the results of the recent study [28] indicate only pseudo-first-order behavior in this region but the true nature should be second order.…”

“…Note also that the TCPs for the four-and nine-spin clusters are located uniquely and their coordinates are (2.4620;-1.0387) and (2.2565;-0.9748), respectively. The values R, = -1.0387 and R, = -0.9748 may be compared to those of the cluster-variation method (R, -1.144) [8,9], Monte Carlo study (R, % -0.9) [14], and recent Monte Carlo approach (R, % -0. 67) [28], On the other hand, for the effective-field theory based on the six-spin cluster there are two possibilities how to select the cluster for the SAF, namely in the horizontal or in the vertical direction (see Fig.…”

Nematic phase in theJ1−J2square-lattice Ising model in an external field

“…In this work we consider J 1 < 0 and J 2 > 0 representing ferromagnetic NN and antiferromagnetic NNN interactions respectively. The competition ratio is defined by κ = At zero external field the model has been extensively studied [14][15][16][17][18][19][20][21][22], considering both ferromagnetic J 1 < 0 and antiferromagnetic J 1 > 0 NN interactions and antiferromagnetic J 2 > 0 NNN interactions. The nature of the thermal phase transition from the stripes to a disordered phase for κ > 1/2 was controversial.…”

Quantum Ising model on the frustrated square lattice

“…In this case, the AF ground-state persists for g < 0.5, while a superantiferromagnetic (SAF) groundstate (characterized by alternated ferromagnetic rows or columns) occurs for g > 0.5 [5]. Moreover, in the absence of transverse fields, the nature of the phase transitions has been clarified only recently, indicating that the * mschmidt@mail.ufsm.br † fabio.zimmer@ufms.br model shows continuous and discontinuous phase transitions as well as tricriticality [5][6][7][8][9][10][11][12][13]. In particular, the thermally driven phase transitions between SAF and PM states are discontinuous for 0.5 < g < g * and continuous for g > g * , where g * locates the tricriticality.…”