Search results for "Square lattice"
showing 10 items of 46 documents
Monte Carlo simulation of phase separation and clustering in the ABV model
1991
As a model for a binary alloy undergoing an unmixing phase transition, we consider a square lattice where each site can be either taken by an A atom, a B atom, or a vacancy (V), and there exists a repulsive interaction between AB nearest neighbor pairs. Starting from a random initial configuration, unmixing proceeds via random jumps of A atoms or B atoms to nearest neighbor vacant sites. In the absence of any interaction, these jumps occur at jump ratesΓ A andΓ B, respectively. For a small concentration of vacancies (c v=0.04) the dynamics of the structure factorS(k,t) and its first two momentsk 1(t),k 2 2 (t) is studied during the early stages of phase separation, for several choices of co…
Two-dimensional isotropic orientational glasses: a computer-simulation study
1989
The analogue of the Edwards-Anderson model for isotropic vector spin glasses, but taking three-component quadrupoles instead of spins at each lattice site, is studied on the square lattice with extensive Monte Carlo calculations, using a nearest-neighbor symmetric gaussian interaction. It is shown that at low temperaturesT the model develops a short range order both with respect to glass like correlations and with respect to “ferromagnetic” correlations among the quadrupoles. The associated correlation lengths and susceptibilities diverge asT→0, and the critical exponents for this zero-temperature phase transition are estimated. Dynamic correlation functions are analyzed as well and it is s…
Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
2016
We elaborate a simple classification scheme of all rank-5 SU(2)-spin rotational symmetric tensors according to i) the on-site physical spin-$S$, (ii) the local Hilbert space $V^{\otimes 4}$ of the four virtual (composite) spins attached to each site and (iii) the irreducible representations of the $C_{4v}$ point group of the square lattice. We apply our scheme to draw a complete list of all SU(2)-symmetric translationally and rotationally-invariant Projected Entangled Pair States (PEPS) with bond dimension $D\leqslant 6$. All known SU(2)-symmetric PEPS on the square lattice are recovered and simple generalizations are provided in some cases. More generally, to each of our symmetry class can…
Fluctuations and lack of self-averaging in the kinetics of domain growth
1986
The fluctuations occurring when an initially disordered system is quenched at timet=0 to a state, where in equilibrium it is ordered, are studied with a scaling theory. Both the mean-sizel(t)d of thed-dimensional ordered domains and their fluctuations in size are found to increase with the same power of the time; their relative size fluctuations are independent of the total volumeLd of the system. This lack of self-averaging is tested for both the Ising model and the φ4 model on the square lattice. Both models exhibit the same lawl(t)=(Rt)x withx=1/2, although the φ4 model has “soft walls”. However, spurious results withx≷1/2 are obtained if “bad” pseudorandom numbers are used, and if the n…
Regular packings on periodic lattices.
2011
We investigate the problem of packing identical hard objects on regular lattices in d dimensions. Restricting configuration space to parallel alignment of the objects, we study the densest packing at a given aspect ratio X. For rectangles and ellipses on the square lattice as well as for biaxial ellipsoids on a simple cubic lattice, we calculate the maximum packing fraction \phi_d(X). It is proved to be continuous with an infinite number of singular points X^{\rm min}_\nu, X^{\rm max}_\nu, \nu=0, \pm 1, \pm 2,... In two dimensions, all maxima have the same height, whereas there is a unique global maximum for the case of ellipsoids. The form of \phi_d(X) is discussed in the context of geomet…
Thermodynamics of the two-dimensional Heisenberg classical honeycomb lattice
1998
In this article we adapt a previous work concerning the two-dimensional (2D) Heisenberg classical square lattice [Physica B 245, 263 (1998)] to the case of a honeycomb lattice. Closed-form expressions of the main thermodynamic functions of interest are derived in the zero-field limit. Notably, near absolute zero (i.e., the critical temperature), we derive the values of the critical exponents $\ensuremath{\alpha}=0,\ensuremath{\eta}=\ensuremath{-}1,\ensuremath{\gamma}=3,$ and $\ensuremath{\nu}=1,$ as for the square lattice, thus proving their universal character. A very simple model allows one to give a good description of the low-temperature behaviors of the product $\ensuremath{\chi}T.$ Fo…
What is the order of the two-dimensional polymer escape transition?
2007
An end-grafted flexible polymer chain in three-dimensional space between two pistons undergoes an abrupt transition from a confined coil to a flowerlike conformation when the number of monomers in the chain, $N$, reaches a critical value. In two-dimensional (2D) geometry, excluded-volume interactions between monomers of a chain confined inside a strip of finite length $2L$ transform the coil conformation into a linear string of blobs. However, the blob picture raises questions about the nature of this escape transition. To check theoretical predictions based on the blob picture we study 2D single-polymer chains with excluded-volume interactions and with one end grafted in the middle of a st…
A universal tensor network algorithm for any infinite lattice
2018
We present a general graph-based Projected Entangled-Pair State (gPEPS) algorithm to approximate ground states of nearest-neighbor local Hamiltonians on any lattice or graph of infinite size. By introducing the structural-matrix which codifies the details of tensor networks on any graphs in any dimension $d$, we are able to produce a code that can be essentially launched to simulate any lattice. We further introduce an optimized algorithm to compute simple tensor updates as well as expectation values and correlators with a mean-field-like effective environments. Though not being variational, this strategy allows to cope with PEPS of very large bond dimension (e.g., $D=100$), and produces re…
Finite-size scaling analysis of the ?4 field theory on the square lattice
1986
Monte-Carlo calculations are performed for the model Hamiltonian ℋ = ∑i[(r/2)Φ 2(i)+(u/4)/gF4(i)]+∑ (C/2)[Φ (i)−Φ(j)]2 for various values of the parametersr, u, C in the crossover region from the Ising limit (r→-∞,u+∞) to the displacive limit (r=0). The variableφ(i) is a scalar continuous spin variable which can lie in the range-∞<φ(i)<+∞, for each lattice site (i).φ(i) is a priori selected proportional to the single-site probability in our Monte Carlo algorithm. The critical line is obtained in very good agreement with other previous approaches. A decrease of apparent critical exponents, deduced from a finite-size scaling analysis, is attributed to a crossover toward mean-field values at t…
Kinetics of domain growth in finite Ising strips
1992
Abstract Monte Carlo simulations are presented for the kinetics of ordering of the two-dimensional nearest-neighbor Ising models in an L x M geometry with two free boundaries of length M ⪢ L . This geometry models a “terrace” of width L on regularly stepped surfaces, adatoms adsorbed on neighboring terraces being assumed to be noninteracting. Starting out with an initially random configuration of the atoms in the lattice gas at coverage θ = 1 2 in the square lattice, quenching experiments to temperatures in the range 0.85⩽ T / T c ⩽1 are considered, assuming a dynamics of the Glauber model type (no conservation laws being operative). At T c the ordering behavior can be described in terms of…