LUTTINGER-LIQUID BEHAVIOUR IN 2D: THE VARIATIONAL APPROACH

1993 ◽  
Vol 07 (03) ◽  
pp. 119-141 ◽  
Author(s):  
CLAUDIUS GROS ◽  
ROSER VALENTÍ
Keyword(s):  
Monte Carlo ◽  
Variational Formulation ◽  
Variational Approach ◽  
Order Parameter ◽  
Luttinger Liquid ◽  
Two Dimensions ◽  
Point Of View ◽  
Two Dimensional ◽  
Liquid Type ◽  
D Wave

We study a variational formulation of the Luttinger-liquid concept in two dimensions. We show that a Luttinger-liquid wavefunction with an algebraic singularity at the Fermiedge is given by a Jastrow-Gutzwiller type wavefunction, which we evaluate by variational Monte Carlo for lattices with up to 38 × 38 = 1444 sites. We therefore find that, from a variational point of view, the concept of a Luttinger liquid is well defined even in 2D. We also find that the Luttinger liquid state is energetically favoured by the projected kinetic energy in the context of the 2D t-J model. We study and find coexistence of d-wave superconductivity and Luttinger-liquid behaviour in two-dimensional projected wavefunctions. We then argue that generally, any two-dimensional d-wave superconductor should be unstable against Luttinger-liquid type correlations along the (quasi-1D) nodes of the d-wave order parameter, at temperatures small compared to the gap.

scholarly journals Interface Roughening in Two Dimensions

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Gernot Münster ◽  
Manuel Cañizares Guerrero
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Capillary Wave ◽  
System Size ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Wave Approximation ◽  
Statistical Field ◽  
Statistical Field Theory ◽  
Interface Roughening

AbstractRoughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of $$w^2$$ w 2 is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of $$w^2$$ w 2 , which differs from results in the literature. It is confirmed by Monte Carlo simulations.

Estimates of critical percolation probabilities for a set of two-dimensional lattices

1972 ◽  
Vol 71 (1) ◽  
pp. 97-106 ◽  
Author(s):  
D. G. Neal
Keyword(s):  
Monte Carlo ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Critical Percolation ◽  
Site Percolation

AbstractThis paper describes new detailed Monte Carlo investigations into bond and site percolation problems on the set of eleven regular and semi-regular (Archimedean) lattices in two dimensions.

scholarly journals Diffusion Monte Carlo Study of Electrons in Two-dimensional Layers

1996 ◽  
Vol 49 (1) ◽  
pp. 161 ◽  
Author(s):  
Francesco Rapisarda ◽  
Gaetano Senatore
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Study ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Diffusion Monte Carlo ◽  
Intermediate Coupling ◽  
Particle Spacing ◽  
Large Coupling ◽  
Liquid Phases ◽  
Fixed Node

We investigate the phase diagram of electrons in two dimensions at T = 0 by means of accurate diffusion Monte Carlo simulations within the fixed-node approximation. At variance with previous studies, we find that in an isolated layer Slater-Jastrow nodes yield stability of the fully polarised fluid at intermediate coupling, before freezing into a triangular crystal sets in. We have also studied coupled layers of electrons and of electrons and holes. Preliminary results show that at large coupling, as two layers are brought together from infinity, inter-layer correlation first stabilises the crystalline phase at distances of the order of the in-plane inter-particle spacing. As the distance is further decreased the effect of correlation, as expected, turns into an enhanced screening, which disrupts the crystalline order in favour of liquid phases.

A NEW METHOD FOR CALCULATING CLASSICAL PERIODIC TRAJECTORIES IN TWO DIMENSIONS

1994 ◽  
Vol 04 (02) ◽  
pp. 251-264 ◽  
Author(s):  
K.T.R. DAVIES
Keyword(s):  
Periodic Orbits ◽  
Gaussian Elimination ◽  
Two Dimensions ◽  
Point Of View ◽  
The Other ◽  
New Method ◽  
Two Dimensional ◽  
Many Body ◽  
Periodic Trajectories ◽  
Dimensional Phase Space

Previously, the monodromy method has been widely used for calculating classical periodic trajectories for a two-dimensional Hamiltonian system, or a four-dimensional phase space. In this paper, the problem is formulated from a different point of view, involving Gaussian-elimination algorithms. Thus, we present a new method for calculating classical periodic orbits, in which each of the basic matrices is of dimension two. Two variants are obtained, one assuming that the period of the motion is fixed and the other assuming that the total energy is fixed. We emphasize the importance of calculating the periodic orbits in as small a dimensionality as possible, an advantage which has implications for generalizations of the theory and methods to outstanding many-body problems in nuclear and atomic physics. Comparisons are made between various approaches.

On the Validation of the Monte Carlo Technique in Simulation of Grain Growth in Small, Two-Dimensional Systems

2007 ◽  
Vol 558-559 ◽  
pp. 1087-1092
Author(s):  
Ola Hunderi ◽  
Knut Marthinsen ◽  
Nils Ryum
Keyword(s):  
Monte Carlo ◽  
Grain Boundary ◽  
Grain Growth ◽  
Computer Simulations ◽  
Two Dimensions ◽  
Theoretical Treatment ◽  
Two Dimensional ◽  
Simulation Techniques ◽  
Boundary Curvature ◽  
Kinetics Of

The kinetics of grain growth in real systems is influenced by several unknown factors, making a theoretical treatment very difficult. Idealized grain growth, assuming all grain boundaries to have the same energy and mobility (mobility M = k/ρ, where k is a constant and ρ is grain boundary curvature) can be treated theoretically, but the results obtained can only be compared to numerical grain growth simulations, as ideal grain growth scarcely exists in nature. The validity of the simulation techniques thus becomes of great importance. In the present investigation computer simulations of grain growth in two dimensions using Monte Carlo simulations and the grain boundary tracking technique have been investigated and compared in small grain systems, making it possible to follow the evolution of each grain in the system.

scholarly journals Refined bounds of the quantum quadratures within the class of distance-disturbed convex functions in two dimensions

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 825-836
Author(s):  
Gabriela Cristescu ◽  
Muhammad Awan ◽  
Mihail Găianu
Keyword(s):  
Finite Elements ◽  
Convex Functions ◽  
Two Dimensions ◽  
Point Of View ◽  
Two Dimensional ◽  
Convexity Properties

In this paper, we introduce the class of disturbed convex functions defined by means of distance perturbations in two dimensions on co-ordinates. Some quantum trapezoidal estimations are obtained for functions having two dimensional distance-disturbed convexity properties. Refined bounds of the quantum integrals of distance-disturbed convex functions on coordinates are deduced by using the rectangular finite elements technique. These approximations are as best as possible from the sharpness point of view. The sharpness of few results from the literature follows as consequence of the new results in this paper.

scholarly journals Dynamic Monte Carlo Study of the Two-Dimensional Quantum XY Model

1998 ◽  
Vol 12 (29n30) ◽  
pp. 1237-1243 ◽  
Author(s):  
H. P. Ying ◽  
H. J. Luo ◽  
L. Schülke ◽  
B. Zheng
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Study ◽  
Two Dimensions ◽  
Xy Model ◽  
Dynamic Scaling ◽  
Two Dimensional ◽  
Time Dynamic ◽  
Dynamic Monte Carlo ◽  
Short Time ◽  
Dynamical Exponents

We present a dynamic Monte Carlo study of the spin-1/2 quantum XY model in two-dimensions at the Kosterlitz–Thouless phase transition temperature. The short-time dynamic scaling behaviour is found and the dynamical exponents θ, z and the static exponent η are determined.

Superluminal coordinate transformations: the two-dimensional case

1983 ◽  
Vol 61 (2) ◽  
pp. 256-263 ◽  
Author(s):  
Louis Marchildon ◽  
Adel F. Antippa ◽  
Allen E. Everett
Keyword(s):  
Time Reversal ◽  
Discrete Symmetries ◽  
Two Dimensions ◽  
Point Of View ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Coordinate Transformations ◽  
The Relationship

This is the first part of a two-paper series, in which we critically examine the various proposals that have been made for superluminal coordinate transformations. Here we consider the two-dimensional case. Starting from rather general assumptions, we show that the superluminal coordinate transformations in two dimensions are essentially uniquely determined. Different proposals for such transformations are then analyzed from the point of view of those assumptions. The relationship between the superluminal transformations and the discrete symmetries P (parity), T (time reversal), and PT is also discussed.

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