We present a fully analytically solvable family of models with many-body cluster interaction and Ising interaction. This family exhibits two phases, dubbed cluster and Ising phases, respectively. The critical point turns out to be independent of the cluster size $n+2$ and is reached exactly when both interactions are equally weighted. For even $n$ we prove that the cluster phase corresponds to a nematic ordered phase and in the case of odd $n$ to a symmetry protected topological ordered phase. Though complex, we are able to quantify the multi-particle entanglement content of neighboring spins. We prove that there exists no bipartite or, in more detail, no $n+1$-partite entanglement. This is possible since the non-trivial symmetries of the Hamiltonian restrict the state space. Indeed, only if the Ising interaction is strong enough (local) genuine $n+2$-partite entanglement is built up. Due to their analytically solvableness the $n$-cluster-Ising models serve as a prototype for studying non trivial-spin orderings and due to their peculiar entanglement properties they serve as a potential reference system for the performance of quantum information tasks.
The J$_1$-J$_2$ Ising model in the square lattice in the presence of an external field is studied by two approaches: the Cluster Variation Method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM…
Many-body systems subject to a high-frequency drive can show intriguing thermalization behavior. Prior to heating to a featureless infinite-temperature state, these systems can spend an exponentially long time in prethermal phases characterized by various kinds of order. Here, we uncover the rich non-equilibrium phase diagram of a driven frustrated two-dimensional Ising magnet with competing short-range ferromagnetic and long-range dipolar interactions. We show that the ordered stripe and nematic phases, which appear in equilibrium as a function of temperature, underpin subsequent prethermal p…
We compute the structure factor of the $J_1$-$J_2$ Ising model in an external field on the square lattice within the Cluster Variation Method. We use a four point plaquette approximation, which is the minimal one able to capture phases with broken orientational order in real space, like the recently reported Ising-nematic phase in the model. The analysis of different local maxima in the structure factor allows us to track the different phases and phase transitions against temperature and external field. Although the nematic susceptibility is not directly related to the structure factor, we sho…
Using a specially designed Monte Carlo algorithm with directed loops, we investigate the triangular lattice Ising antiferromagnet with coupling beyond nearest neighbour. We show that the first-order transition from the stripe state to the paramagnet can be split, giving rise to an intermediate nematic phase in which algebraic correlations coexist with a broken symmetry. Furthermore, we demonstrate the emergence of several properties of a more topological nature such as fractional edge excitations in the stripe state, the proliferation of double domain walls in the nematic phase, and the Kastel…
Active nematics are conceptually the simplest orientationally ordered phase of self-driven particles, but have proved to be a perennial source of surprises. We show here through numerical solution of coarse-grained equations for order parameter and density that the growth of the active nematic phase from the isotropic phase is necessarily accompanied by a clumping of the density. The growth kinetics of the density domains is shown to be faster than the 1/3-law expected for variables governed by a conservation law. Other results presented include the suppression of density fluctuations in the s…
Previous studies show that, in quantum chaotic and integrable systems, the so-called out-of-time-ordered correlator (OTOC) generically behaves differently at long times, while, it may show similar early growth in one-body systems. In this paper, by means of numerical simulations, it is shown that OTOC has similar early growth in two quantum many-body systems, one integrable and one chaotic.
Critical behavior of the two-dimensional generalized $XY$ model involving solely nematic-like terms of the second, third and fourth orders is studied by Monte Carlo method. We find that such a system can undergo three successive phase transitions. At higher temperatures there is a phase transition of the Berezinskii-Kosterlitz-Thouless type to the $q=4$ nematic-like phase, followed by two more transitions of the Ising type to the $q=2$ nematic-like and ferromagnetic phases, respectively. The $q$ nematic-like phases are characterized by spin alignments with angles $2kπ/q$, where $k \leq q$ is a…
In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, $m_2<m_3 < \dots$. Each ratio $m_{2,3,\dots}/m_1$ ($m_1$: the single-magnon mass) is expected to be a universal constant in the vicinity of the critical point. In this paper, we devote ourselves to the $(2+1)$-dimensional counterpart, for which the universal hierarchical character remains unclear. We employed the exact diagonalization method, which enables us to calculate the dynamical susceptibility via the continued-fraction expansion. Thereby, we observe a variety o…
We formulate the statistical dynamics of topological defects in the active nematic phase, formed in two dimensions by a collection of self-driven particles on a substrate. An important consequence of the non-equilibrium drive is the spontaneous motility of strength +1/2 disclinations. Starting from the hydrodynamic equations of active nematics, we derive an interacting particle description of defects that includes active torques. We show that activity, within perturbation theory, lowers the defect-unbinding transition temperature, determining a critical line in the temperature-activity plane t…
We examine dense self-gravitating stellar systems dominated by a central potential, such as nuclear star clusters hosting a central supermassive black hole. Different dynamical properties of these systems evolve on vastly different timescales. In particular, the orbital-plane orientations are typically driven into internal thermodynamic equilibrium by vector resonant relaxation before the orbital eccentricities or semimajor axes relax. We show that the statistical mechanics of such systems exhibit a striking resemblance to liquid crystals, with analogous ordered-nematic and disordered-isotropi…
Determination of the Critical Exponents for the Isotropic-Nematic Phase Transition in a System of Long Rods on Two-dimensional Lattices: Universality of the Transition
CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solver
University of Rochester（罗切斯特大学）；Northwestern University（西北大学）；University of Maryland（马里兰大学）；National Center for Theoretical Sciences（国家理论科学中心）；HonHai (Foxconn) Research Institute（鸿海研究院）
A system of hard rectangles of size $m\times mk$ on a square lattice undergoes three entropy driven phase transitions with increasing density for large enough aspect ratio $k$: first from a low density isotropic to an intermediate density nematic phase, second from the nematic to a columnar phase, and third from the columnar to a high density sublattice phase. In this paper we show, from extensive Monte Carlo simulations of systems with $m=1,2$ and $3$, that the transition density for the isotropic-nematic transition is $\approx A_1/k$ when $k \gg 1$, where $A_1$ is independent of $m$. We esti…
We study Ising pyrochlores by means of Monte Carlo simulations. We cover a set of exchange constants ranging from the frustrated ferromagnetic case (spin-ice) to the fully-ordered "all-in--all-out" antiferromagnet in the dipolar model, reinterpreting the results --as in an ionic system-- in terms of a temperature vs. magnetic charge density phase diagram. In spite of its spin nature and the presence of both double and single non-conserved magnetic charges, the dipolar model gives place to a phase diagram which is quite comparable with those previously obtained for on-lattice systems of electri…
