First-order transition and marginal critical behavior in a novel 2D frustrated Ising model

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

   A. Kalz, A. Honecker, M. Moliner · 2011 · Physical Review B · cited 40 times · Not summarized yet

   Abstract

   We analyze the phase transition of the frustrated $J_1$-$J_2$ Ising model with antiferromagnetic nearest- and strong next-nearest neighbor interactions on the square lattice. Using extensive Monte Carlo simulations we show that the nature of the phase transition for $1/2 < J_2/J_1 \lesssim 1$ 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…

2. Very close Cited by this paper Not relevant

   A comprehensive study of the phase transitions of the frustrated J1-J2 Ising model on the square lattice

   Shang-Wei Li, Fu-Jiun Jiang · 2024 · Progress of Theoretical and Experimental Physics · cited 14 times · Not summarized yet

   Abstract

   We study the phase transitions of the two-dimensional frustrated J1-J2 Ising model on the square lattice with Monte Carlo simulations. Here J1 < 0 and J2 > 0 are the couplings for the nearest and next nearest neighbor Ising spins, respectively. In addition, we consider J1 = −1 and J2/|J1| ≡ g = 0.56, 0.58, 0.60, 0.62, 0.64 and 0.7 in our investigation. Several physical quantities including the Binder ratio U, the specific heat Cv, and the energy density E are obtained. The analyses of these calculated observables indicate that the considered phase transitions for g ≥ 0.58 are likely second order, and the nature of the phase transition associated with g = 0.56 needs further investigation. A c…

3. Very close Cited by this paper Not relevant

   Tensor network simulation for the frustrated J_{1}-J_{2} Ising model on the square lattice.

   Hong Li, Li-Ping Yang · 2021 · Physical Review E · cited 28 times · Not summarized yet

   Abstract

   By using extensive tensor network calculations, we map out the phase diagram of the frustrated J_{1}-J_{2} Ising model on the square lattice. In particular, we focus on the cases with controversy in the phase diagram, especially the stripe transition in the regime g=|J_{2}/J_{1}|>1/2 (J_{2}>0,J_{1}<0). While recent studies claimed that the phase transition is of first order when 1/2<g<g^{*} (with the smallest g^{*} being 0.67), our simulations suggest that if there is such a first-order region, it is smaller than those found in earlier studies by other methods. Combining with the analysis of critical properties, we provide evidence that the classical J_{1}-J_{2} model evolves continuously fr…

4. Very close Cited by this paper Not relevant

   Phase transitions in the frustrated Ising model on the square lattice

   Songbo Jin, Arnab Sen, Wen-An Guo et al. · 2012 · Physical Review B · cited 96 times · Not summarized yet

   Abstract

   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 (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 s…

5. Very close Cited by this paper Not relevant

   Location of the Potts-critical end point in the frustrated Ising model on the square lattice

   A. Kalz, A. Honecker · 2012 · Physical Review B · cited 47 times · Not summarized yet

   Abstract

   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 …

6. Very close Cites this paper Not relevant

   Tensor renormalization-group study of the surface critical behavior of a frustrated two-layer Ising model

   Christophe Chatelain · 2025 · Journal of Statistical Mechanics: Theory and Experiment · Not summarized yet

   Abstract

   Two replicas of a 2D Ising model are coupled by frustrated spin-spin interactions. It is known that this inter-layer coupling is marginal and that the bulk critical behavior belongs to the Ashkin–Teller (AT) universality class, as the J1−J2 Ising model. In this work, the surface critical behavior is studied numerically by tensor renormalization-group calculations. The bond-weight tensor renormalization group algorithm is extended to tackle systems with boundaries. It is observed that the two-fold degeneracy of the surface magnetic scaling dimension of the AT model is lifted in the frustrated two-layer Ising model (F2LIM). The splitting is explained by the breaking of the Z2-symmetry under sp…

7. Very close Cites this paper Not relevant

   Competing ferromagnetic and antiferromagnetic phases on the frustrated Ising honeycomb lattice

   P. F. Dias, F. Zimmer, N. G. Fytas et al. · 2026 · Physica A: Statistical Mechanics and its Applications · cited 4 times · Not summarized yet

   Abstract

   We investigate the frustrated $J_1$-$J_2$-$J_3$ Ising model on the honeycomb lattice, featuring first- and second-neighbor ferromagnetic couplings ($J_1>0$ and $J_2>0$) and third-neighbor antiferromagnetic interactions ($J_3<0$). Using the cluster mean-field method, we analyze the phase transitions in the regime $1/2<J_2/J_1 \le 1$, where ferromagnetic and antiferromagnetic phases compete. Our results reveal that near the strongly frustrated limit $J_3/J_1 = -1$, the system exhibits order-by-disorder state selection, tricritical and bicritical behavior, critical endpoints, and two successive phase transitions. The ferromagnetic-paramagnetic transition remains second order across the entire i…

8. Very close Cited by this paper Not relevant

   Higher-order tensor renormalization group study of the $J_1$-$J_2$ Ising model on a square lattice

   Kota Yoshiyama, Koji Hukushima · 2023 · cited 18 times · Not summarized yet

   Abstract

   Phase transitions of the $J_1$-$J_2$ Ising model on a square lattice are studied using the higher-order tensor renormalization group(HOTRG) method. This system involves a competition between the ferromagnetic interaction $J_1$ and antiferromagnetic interaction $J_2$. Furthermore, weak first-order and second-order transitions are observed near the ratio $g=J_2/|J_1|=1/2$. Our results (based on HOTRG calculations for significantly larger sizes) indicate that the region of the first-order transition is marginally narrower than that in previous studies. Moreover, the universality class of the second-order transition connected to the transition line is not necessarily fully consistent with the As…

Prior work it builds on

1. Close* Not relevant

   Phase diagrams and critical behavior in Ising square lattices with nearest- and next-nearest-neighbor interactions

   K. Binder, D. Landau · 1980 · Physical Review B · cited 326 times · Not summarized yet
2. Close Not relevant

   CTMRG study of the critical behavior of an interacting-dimer model

   Christophe Chatelain · 2024 · Journal of Statistical Mechanics: Theory and Experiment · cited 1 time · Not summarized yet

   Abstract

   The critical behavior of a dimer model with an interaction favoring parallel dimers in each plaquette of the square lattice is studied numerically using the corner transfer matrix renormalization group algorithm. The critical exponents are known to depend on the chemical potential of vacancies, or monomers. At large average density of the latter, the phase transition becomes the first-order. We compute the scaling dimensions of both the order parameter and temperature in the second-order regime and compare them with the conjecture that the critical behavior is the same as the Ashkin–Teller model on its self-dual critical line.

3. Close Not relevant

   Tensor network based finite-size scaling for two-dimensional Ising model

   Ching-Yu Huang, S. Chan, Y. Kao et al. · 2023 · Physical review B · cited 10 times · Not summarized yet

   Abstract

   We propose a scheme to perform tensor network based finite-size scaling analysis for two-dimensional classical models. In the tensor network representation of the partition function, we use higher-order tensor renormalization group (HOTRG) method to coarse grain the weight tensor. The renormalized tensor is then used to construct the approximated transfer matrix of an infinite strip of finite width. By diagonalizing the transfer matrix we obtain the correlation length, the magnetization, and the energy density which are used in finite-size scaling analysis to determine the critical temperature and the critical exponents. As a benchmark we study the two-dimensional classical Ising model. We s…

4. Close* Not relevant

   Phase transitions in Ising square antiferromagnets with first- and second-neighbour interactions

   J. Morán-López, F. Aguilera-Granja, Juan M. Sanchez · 1994 · Journal of Physics: Condensed Matter · cited 35 times · Not summarized yet
5. Close* Not relevant

   Monte Carlo renormalization group and Ising models with n > or = 2

   R. H. Swendsen, S. Krinsky · 1979 · Physical Review Letters · cited 89 times · Not summarized yet

Papers that cite it

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   Relevant-marginal field mixing resolves the four-state Potts endpoint in the square-lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi>

   Yi-Hua Sun, Yucheng Fan · 2026 · Physical review B · Not summarized yet

   Abstract

   Identifying endpoint criticality is challenging because pseudo-first-order signatures can persist over accessible system sizes and obscure the underlying scaling behavior. This difficulty is especially acute in the frustrated square-lattice \(J_1\)--\(J_2\) Ising model, where the location and even the nature of the stripe-ordering endpoint have remained controversial for decades. Here we treat this endpoint as a relevant--marginal two-field scaling problem and develop a generalized field-mixing construction to resolve the endpoint ambiguity. Mixed-histogram symmetry defines a finite-size pseudotransition manifold, transforming pseudo-first-order finite-size structure into a scaling trajector…

2. Related* Not relevant

   Long-Range Interactions in 1D Adsorption Models: Tensor Network Approach

   Anastasiia V. Karpova, A. I. Uliankina, V. Gorbunov et al. · 2026 · Journal of statistical physics · Not summarized yet