Related papers: Macroscopic Degeneracy and order in the 3d plaquet…
We review some recent investigations of the 3d plaquette Ising model. This displays a strong first-order phase transition with unusual scaling properties due to the size-dependent degeneracy of the low-temperature phase. In particular, the…
It is known that fixed boundary conditions modify the leading finite-size corrections for an L^3 lattice in 3d at a first-order phase transition from 1/L^3 to 1/L. We note that an exponential low-temperature phase degeneracy of the form…
In this paper we conduct a careful multicanonical simulation of the isotropic $3d$ plaquette ("gonihedric") Ising model and confirm that a planar, fuki-nuke type order characterises the low-temperature phase of the model. From consideration…
A 3D Ising model with a purely plaquette, 4-spin interaction displays a planar flip symmetry intermediate between a global and a gauge symmetry and as a consequence has a highly degenerate low temperature phase and no standard magnetic…
We note that the standard inverse system volume scaling for finite-size corrections at a first-order phase transition (i.e., 1/L^3 for an L x L x L lattice in 3D) is transmuted to 1/L^2 scaling if there is an exponential low-temperature…
We examine the ordering behavior of the ferromagnetic Ising lattice model defined on a surface with a constant negative curvature. Small-sized ferromagnetic domains are observed to exist at temperatures far greater than the critical…
We study a stacked triangular lattice Ising model with both intra- and inter-plane antiferromagnetic interactions in a field, by Monte Carlo simulation. We find only one phase transition from a paramagnetic to a partially disordered phase,…
Geometrically frustrated materials have a ground-state degeneracy that may be lifted by subtle effects, such as higher order interactions causing small energetic preferences for ordered structures. Alternatively, ordering may result from…
In the corner-sharing lattice, magnetic frustration causes macroscopic degeneracy in the ground state, which prevents systems from ordering. However, if the ensemble of the degenerate configuration has some global structure, the system can…
We employ the microcanonical inflection-point analysis method, developed for the systematic identification and classification of phase transitions in systems of any size, to study the two-dimensional Ising model at various lattice sizes and…
A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model…
In a previous paper [Phys. Rev. E 90, 022506 (2014)], we had studied thermodynamic and structural properties of a three-dimensional simple-cubic lattice model with dipolar-like interaction, truncated at nearest-neighbor separation, for…
We study a family of models for an $N_1 \times N_2$ matrix worth of Ising spins $S_{aB}$. In the large $N_i$ limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single…
An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (Phys. Rev. Lett. 28 (1972) 507), who later dubbed it the fuki-nuke,…
At low temperatures, some lattice spin models with simple ferromagnetic or antiferromagnetic interactions (for example nearest-neighbour interaction being isotropic in spin space on a bipartite three-dimensional lattice) produce…
Discrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric, ferromagnetic or antiferromagnetic, including off-diagonal disorder, are studied, for the number of states $q=3,4$ in $d$…
We perform intensive numerical simulations of the three-dimensional site-diluted Ising antiferromagnet in a magnetic field at high values of the external applied field. Even if data for small lattice sizes are compatible with second-order…
Using extensive classical and quantum Monte Carlo simulations, we investigate the ground-state phase diagram of the fully frustrated transverse field Ising model on the square lattice. We show that pure columnar order develops in the…
The gonihedric Ising Hamiltonians defined in three and higher dimensions by Savvidy and Wegner provide an extensive, and little explored, catalogue of spin models on (hyper)cubic lattices with many interesting features. In three dimensions…
Using extensive Monte Carlo simulations, we clarify the critical behaviour of the 3 dimensional simple cubic Ising Fully Frustrated system. We find two transition temperatures and two long range ordered phases. Within the present numerical…