arXiv:2104.12517 · Journal of Statistical Mechanics Theory and Experiment

Four-point interfacial correlation functions in two dimensions. Exact results from field theory and numerical simulations

Alessio Squarcini, Antonio Tinti

Published Oct 1, 2021• 10 citations

Abstract

Abstract We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip and found to be in excellent agreement with high-precision Monte Carlo simulations.

DOI: 10.1088/1742-5468/ac257c

Related papers

Correlations and structure of interfaces in the Ising model: theory and numerics

Alessio Squarcini, Antonio Tinti

Abstract We consider phase separation on the strip for the two-dimensional Ising model in the near-critical region. Within the framework of field theory, we find exact analytic results for certain two- and three-point correlation functions of the order parameter field. The analytic results for order parameter correlations, energy density profile, subleading corrections and passage probability density of the interface are confirmed by accurate Monte Carlo simulations we performed.

arXiv:2104.06660Journal of Statistical Mechanics Theory and ExperimentAug 1, 202115 citations

Multipoint correlation functions at phase separation. Exact results from field theory

Alessio Squarcini

Abstract We consider near-critical two-dimensional statistical systems with boundary conditions inducing phase separation on the strip. By exploiting low-energy properties of two-dimensional field theories, we compute arbitrary n-point correlation of the order parameter field. Finite-size corrections and mixed correlations involving the stress tensor trace are also discussed. As an explicit illustration of the technique, we provide a closed-form expression for a three-point correlation function and illustrate the explicit form of the long-ranged interfacial fluctuations as well as their confinement within the interfacial region.

arXiv:2104.05073Journal of High Energy PhysicsNov 12, 202110 citations

Droplet-mediated long-range interfacial correlations. Exact field theory for entropic repulsion effects

Alessio Squarcini, Antonio Tinti

Abstract We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of two-dimensional field theories are used in order to find exact analytic results for one- and two-point correlation functions of both the energy density and order parameter fields. The subleading finite-size corrections are also computed and interpreted within an exact probabilistic picture in which interfacial fluctuations are characterized by the probability density of a Brownian excursion. The explicit analysis of the closed-form expression for order parameter correlations reveals the long-ranged character of interfacial correlations and their confinement within the interfacial region. The analysis of correlations is then carried out in momentum space through the notion of interface structure factor, which we extend to the case of systems bounded by a flat wall. The presence of the wall and its associated entropic repulsion leads to a specific term in the interface structure factor which we identify.

arXiv:2106.01945Journal of High Energy PhysicsMar 17, 20237 citations

The four dimensional site-diluted Ising model: a finite-size scaling study

H.G. Ballesteros, L. A. Fernández, Víctor Martín-Mayor +4 more

Using finite-size scaling techniques, we study the critical properties of the site-diluted Ising model in four dimensions. We carry out a high-statistics Monte Carlo simulation for several values of the dilution. The results support the perturbative scenario: there is only the Ising fixed point with large logarithmic scaling corrections. We obtain, using the Perturbative Renormalization Group, functional forms for the scaling of several observables that are in agreement with the numerical data.

Jan 1, 199732 citations

RECENT RESULTS OF MULTIMAGNETICAL SIMULATIONS OF THE ISING MODEL

Ulrich H. E. Hansmann, Bernd A. Berg, T. Neuhaus

To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the 2D and 3D Ising model. Stringent tests of the numerical methods are performed by reproducing with high precision exact 2D results. In the physically more interesting 3D case we estimate the amplitude [Formula: see text] of the critical interfacial tension.

arXiv:hep-lat/9207007International Journal of Modern Physics COct 1, 19928 citations

Three-dimensional randomly dilute Ising model: Monte Carlo results

Pasquale Calabrese, Víctor Martín-Mayor, Andrea Pelissetto C +1 more

We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices L3 with L< or =256. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining nu=0.683(3), eta=0.035(2), beta=0.3535(17), and alpha=-0.049(9), in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio R(+)(xi) that expresses the universality of the free-energy density per correlation volume. We find R(+)(xi)=0.2885(15).

arXiv:cond-mat/0306272Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsSep 30, 200353 citations