We investigate the full phase diagram of the frustrated J1-J2 Ising model on the two-dimensional honeycomb lattice, incorporating both nearest-neighbor interaction J1 and next-nearest-neighbor interaction J2 using the Wang–Landau Monte Carlo method combined with finite-size scaling analysis. We map out the zero- and finite-temperature phase diagrams as a function of J2/J1. From the entropy profile, we identify four distinct ground-state structures — ferromagnetic, antiferromagnetic, dimer, and stripe states — and confirm that the residual entropy scales linearly with the lattice’s linear dimension in the stripe and dimer ground states. Our results suggest that the transition from the paramagnetic phase into the dimer or stripe phase changes its nature from first-order to continuous while the transition into the ferromagnetic or antiferromagnetic phase is continuous and belongs to the two-dimensional Ising universality class.

Schelling's segregation model demonstrates how simple local rules can generate large-scale social patterns, yet it assumes agents act myopically and ignore the broader consequences of their moves. We extend this framework by introducing social orientation as a behavioral microfoundation, reflecting humans' communal nature. Socially oriented agents follow boundedly rational heuristics that account for the satisfaction of prospective neighbors within a two-step horizon of observability, in addition to their own. We formalize this through three relocation rules-negative externality avoiding (NEA), positive externality favoring (PEF), and positive externality optimizing (PEO)-each capturing a different balance between minimizing disruption and promoting stability. Agent-based simulations reveal that these rules, while maintaining satisfaction, consistently reduce segregation, accelerate the attainment of global stability, and lower relocation moves per agent, thereby reducing social costs. These results provide a stronger behavioral foundation for segregation modeling and show how locally rational, socially sensitive decision-making can scale into equilibria that are not just welfare-enhancing but also yield more integrated and resilient communities.

We study the phase transitions and the critical behavior of the Ising and Blume–Capel models on two kinds of two-dimensional Penrose tiles employing Monte Carlo methods and detailed finite-size scaling analysis. The Wolff algorithm is used for the Ising model whereas the Wang–Landau and Metropolis algorithms are used for the Blume–Capel model to obtain critical temperatures and exponents. The phase diagram of the Blume–Capel model reveals the presence of the double transition, the reentrant behavior, and the tricriticality in the vicinity of the critical single-ion anisotropy. Our results indicate that continuous phase transitions of the Ising and Blume–Capel models on the Penrose tiles belong to the two-dimensional Ising universality class. However, the scaling functions depend on the spin magnitude, anisotropy, and graph shape. Lastly, we verify that the critical Binder cumulant is also universal but depends on the shape of the graph.

We investigate the full phase diagram of the frustrated J1-J2 Ising model on the two-dimensional honeycomb lattice, incorporating both nearest-neighbor interaction J1 and next-nearest-neighbor interaction J2 using the Wang–Landau Monte Carlo method combined with finite-size scaling analysis. We map out the zero- and finite-temperature phase diagrams as a function of J2/J1. From the entropy profile, we identify four distinct ground-state structures — ferromagnetic, antiferromagnetic, dimer, and stripe states — and confirm that the residual entropy scales linearly with the lattice’s linear dimension in the stripe and dimer ground states. Our results suggest that the transition from the paramagnetic phase into the dimer or stripe phase changes its nature from first-order to continuous while the transition into the ferromagnetic or antiferromagnetic phase is continuous and belongs to the two-dimensional Ising universality class.

Schelling's segregation model demonstrates how simple local rules can generate large-scale social patterns, yet it assumes agents act myopically and ignore the broader consequences of their moves. We extend this framework by introducing social orientation as a behavioral microfoundation, reflecting humans' communal nature. Socially oriented agents follow boundedly rational heuristics that account for the satisfaction of prospective neighbors within a two-step horizon of observability, in addition to their own. We formalize this through three relocation rules-negative externality avoiding (NEA), positive externality favoring (PEF), and positive externality optimizing (PEO)-each capturing a different balance between minimizing disruption and promoting stability. Agent-based simulations reveal that these rules, while maintaining satisfaction, consistently reduce segregation, accelerate the attainment of global stability, and lower relocation moves per agent, thereby reducing social costs. These results provide a stronger behavioral foundation for segregation modeling and show how locally rational, socially sensitive decision-making can scale into equilibria that are not just welfare-enhancing but also yield more integrated and resilient communities.

We study the phase transitions and the critical behavior of the Ising and Blume–Capel models on two kinds of two-dimensional Penrose tiles employing Monte Carlo methods and detailed finite-size scaling analysis. The Wolff algorithm is used for the Ising model whereas the Wang–Landau and Metropolis algorithms are used for the Blume–Capel model to obtain critical temperatures and exponents. The phase diagram of the Blume–Capel model reveals the presence of the double transition, the reentrant behavior, and the tricriticality in the vicinity of the critical single-ion anisotropy. Our results indicate that continuous phase transitions of the Ising and Blume–Capel models on the Penrose tiles belong to the two-dimensional Ising universality class. However, the scaling functions depend on the spin magnitude, anisotropy, and graph shape. Lastly, we verify that the critical Binder cumulant is also universal but depends on the shape of the graph.

Networks are ubiquitous in various fields, representing systems where nodes and their interconnections constitute their intricate structures. We introduce a network decomposition scheme to reveal multiscale core-periphery structures lurking inside, using the concept of locally defined nodal hub centrality and edge-pruning techniques built upon it. We demonstrate that the hub-centrality-based edge pruning reveals a series of breaking points in network decomposition, which effectively separates a network into its backbone and shell structures. Our local-edge decomposition method iteratively identifies and removes locally least connected nodes, and uncovers an onionlike hierarchical structure as a result. Compared with the conventional k-core decomposition method, our method based on relative information residing in local structures exhibits a clear advantage in terms of discovering locally crucial substructures. As an application of the method, we present a scheme to detect multiple core-periphery structures and the decomposition of coarse-grained supernode networks, by combining the method with the network community detection.

We investigate a family of generalized ice models, employing Wang-Landau Monte Carlo sampling to characterize their residual entropies and thermodynamic behaviors. For the edge-sharing square-ice model, we derive an exact residual-entropy formula. Pauling's approximation yields semiquantitative agreement for corner-sharing systems, typically underestimating residual entropy, but notably overestimating it in the corner-sharing hexagonal-ice model. Thermodynamic analysis reveals that the models with extensive residual entropy exhibit Schottky-type specific heat, without indications of phase transitions, whereas the edge-sharing square-ice and face-sharing cubic-ice models show signatures of continuous and first-order finite-temperature phase transitions, respectively. These results demonstrate how ice-rule constraints give rise to diverse thermodynamic phenomena and offer insights into related frustrated systems.

Abstract We investigate the frustrated J 1 – J 2 Ising model with nearest-neighbor interaction J 1 and next-nearest-neighbor interaction J 2 in two kinds of generalized triangular lattices (GTLs) employing the Wang–Landau Monte Carlo method and finite-size scaling analysis. In the first GTL (GTL1), featuring anisotropic properties, we identify three kinds of super-antiferromagnetic ground states with stripe structures. Meanwhile, in the second GTL (GTL2), which is non-regular in next-nearest-neighbor interaction, the ferrimagnetic 3×3 and two kinds of partial spin liquid (PSL) ground states are observed. We confirm that residual entropy is proportional to the number of spins in the PSL ground states. Additionally, we construct finite-temperature phase diagrams for ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. In GTL1, the transition into the ferromagnetic phase is continuous, contrasting with the first-order transition into the stripe phase. In GTL2, the critical temperature into the ferromagnetic ground state decreases as antiferromagnetic next-nearest-neighbor interaction intensifies until it meets the 3×3 phase boundary. For intermediate values of the next-nearest-neighbor interaction, two successive transitions emerge: one from the paramagnetic phase to the ferromagnetic phase, followed by the other transition from the ferromagnetic phase to the 3×3 phase.