Finite-Size Scaling in Two-Dimensional Superfluids

Abstract

Using the $x-y$ model and a non-local updating scheme called cluster Monte Carlo, we calculate the superfluid density of a two dimensional superfluid on large-size square lattices $L\times L$ up to $400\times 400$. This technique allows us to approach temperatures close to the critical point, and by studying a wide range of $L$ values and applying finite-size scaling theory we are able to extract the critical properties of the system. We calculate the superfluid density and from that we extract the renormalization group beta function. We derive finite-size scaling expressions using the Kosterlitz-Thouless-Nelson Renormalization Group equations and show that they are in very good agreement with our numerical results. This allows us to extrapolate our results to the infinite-size limit. We also find that the universal discontinuity of the superfluid density at the critical temperature is in very good agreement with the Kosterlitz-Thouless-Nelson calculation and experiments.

13 pages, postscript file

Cited by in corpus (40)

• Similarity of fluctuations in correlated systems: The case of seismicity
• The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
• Nematic phase of the two-dimensional electron gas in a magnetic field
• Quantum Monte Carlo study of S=1/2 weakly-anisotropic antiferromagnets on the square lattice
• Classical Phase Fluctuations in High Temperature Superconductors
• Computing the Roughening Transition of Ising and Solid-On-Solid Models by BCSOS Model Matching
• Finite-size scaling method for the Berezinskii-Kosterlitz-Thouless transition
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Path integral Monte Carlo simulation of the second layer of helium-4 adsorbed on graphite
• The Kosterlitz-Thouless Universality Class
• Flux lattice melting and depinning in the weakly frustrated 2D XY model
• The isotropic-to-nematic transition in a two-dimensional fluid of hard needles : a finite-size scaling study
• Nonperturbative renormalization group treatment of amplitude fluctuations for $|\phi {|}^4$ topological phase transitions
• Long-range phase order in two dimensions under shear flow
• Crossover from Two- to Three-Dimensional Behavior in Superfluids
• High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensional XY model
• A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models
• Phase transitions and autocorrelation times in two-dimensional Ising model with dipole interactions
• BKT universality class in the presence of correlated disorder
• Superconductivity Versus Phase Separation, Stripes, and Checkerboard Ordering: A Two-Dimensional Monte Carlo Study
• Scaling of thermal conductivity of helium confined in pores
• Boundary effects in superfluid films
• Topological magnetic phase transition in Eu-based A-type antiferromagnets
• Self-consistent harmonic approximation with non-local couplings
• Thermal excitations of frustated XY spins in two dimensions
• Quantum Monte Carlo Study on the Spin-1/2 Honeycomb Heisenberg Model with Mixing Antiferromagnetic and Ferromagnetic Interactions in External Magnetic Fields
• Reentrance of Berezinskii-Kosterlitz-Thouless-like transitions in three-state Potts antiferromagnetic thin film
• Finite Temperature Off-Diagonal Long-Range Order for Interacting Bosons
• Percolation of the two-dimensional XY model in the flow representation
• Hidden degree of freedom and critical states in a two-dimensional electron gas in the presence of a random magnetic field
• Signatures of thermally excited vortices in a superconductor with competing orders
• Superfluid Spin Transistor
• Non-equilibrium vortex annealing of structural disorder in Berezinskii-Kosterlitz-Thouless dynamics of two-dimensional XY-model
• Spin Hall effect of vorticity
• Topological charge scaling at a quantum phase transition
• Inhomogeneous phase stiffness in two-dimensional $s$-wave disordered superconductors
• Machine learning analysis of dimensional reduction conjecture for nonequilibrium Berezinskii-Kosterlitz-Thouless transition in three dimensions
• Apparent double-$T_c$ from a single BKT transition in anisotropic phase-only models
• Universal non-power-law scaling from a chaotic renormalisation group in the Harper-Hofstadter model
• Object orientation and visualization of physics in two dimensions