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

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Alessio Squarcini
Keyword(s):  
Phase Separation ◽  
Finite Size ◽  
Closed Form Expression ◽  
Interfacial Region ◽  
Two Dimensional ◽  
Parameter Field ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Statistical Systems ◽  
Finite Size Corrections

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.

Transfer Matrix Study of Finite-size Corrections in the 2D Ising Model

2005 ◽  
Vol 5 (1) ◽  
pp. 72-85 ◽  
Author(s):  
J. Kaupužs
Keyword(s):  
Correlation Function ◽  
Ising Model ◽  
Transfer Matrix ◽  
Finite Size ◽  
Lattice Systems ◽  
Small Magnitude ◽  
Amplitude Correction ◽  
Matrix Algorithms ◽  
Point Correlation ◽  
Point Correlation Function

AbstractEffective exact transfer matrix algorithms have been developed to compute the two-point correlation function G(r) of the 2D Ising model on a square finite size lattice. Systems including up to 800 spins have been considered and corrections to the finite-size scaling at the critical point have been analysed.As a new result, we have found that the correlation function has a nontrivial amplitude correction of a very small magnitude.

NUMERICAL STUDY OF A TWO-POINT CORRELATION FUNCTION AND LIOUVILLE FIELD PROPERTIES IN TWO-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (12) ◽  
pp. 1115-1131 ◽  
Author(s):  
M.E. AGISHTEIN ◽  
R. BENAV ◽  
A.A. MIGDAL ◽  
S. SOLOMON
Keyword(s):  
Correlation Function ◽  
Quantum Gravity ◽  
Green's Function ◽  
Field Model ◽  
Numerical Study ◽  
Free Field ◽  
Sampling Technique ◽  
Two Dimensional ◽  
Point Correlation ◽  
Point Correlation Function

Two-point Green’s function is measured on the manifolds of a 2-dimensional quantum gravity. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to hundred thousand triangles. The grid Laplacian was inverted by means of the algebraic multi-grid solver. The free field model of the Quantum Gravity assumes the Gaussian behavior of Liouville field and curvature. We measured histograms as well as six momenta of these fields. Our results support the Gaussian assumption.

scholarly journals Finite-size corrections in the bosonic algebraic approach to two-dimensional systems

2011 ◽  
Vol 83 (6) ◽  
Author(s):  
P. Pérez-Fernández ◽  
José M. Arias ◽  
J. E. García-Ramos ◽  
F. Pérez-Bernal
Keyword(s):  
Finite Size ◽  
Algebraic Approach ◽  
Two Dimensional ◽  
Finite Size Corrections

scholarly journals Galaxy Clustering to B = 27M

1994 ◽  
Vol 161 ◽  
pp. 635-643
Author(s):  
N. Roche ◽  
T. Shanks ◽  
N. Metcalfe ◽  
R. Fong
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Redshift Distribution ◽  
Galaxy Clustering ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Luminosity Evolution

The angular two-point correlation function, ω(θ), for galaxies can be used as a probe of their redshift distribution N(z) and, therefore, of galaxy luminosity evolution. Without redshift data, we can still observe the projection onto the two-dimensional sky of the three-dimensional clustering of galaxies. The autocorrelation of this projected distribution is described by ω(θ). Observations have indicated that ω(θ) follows a θ−0.8 power-law (Peebles 1980) and that the index of the power-law remains approximately constant to the faintest limits of photographic surveys (Jones, Shanks & Fong 1987).

scholarly journals A topological transition by confinement of a phase separating system with radial quenching

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Tsuyoshi Tsukada ◽  
Rei Kurita
Keyword(s):  
Phase Separation ◽  
Finite Size ◽  
Finite Size Effect ◽  
Two Dimensional ◽  
Spatial Confinement ◽  
Topological Transition ◽  
One Dimensional ◽  
Equilibrium Processes ◽  
Layered Pattern ◽  
Quenched Systems

Abstract Physicochemical systems are strongly modified by spatial confinement; the effect is more pronounced the stronger the confinement is, making its influence particularly important nanotechnology applications. For example, a critical point of a phase transition is shifted by a finite size effect; structure can be changed through wetting to a container wall. Recently, it has been shown that pattern formation during a phase separation is changed when a system is heterogeneously quenched instead of homogeneously. Flux becomes anisotropic due to a heterogeneous temperature field; this suggests that the mechanism behind heterogeneous quenching is different from that of homogeneous quenching. Here, we numerically study the confinement effect for heterogeneously quenched systems. We find that the pattern formed by the phase separation undergoes a topological change with stronger confinement i.e. when the height of a simulation box is varied, transforming from a one-dimensional layered pattern to a two-dimensional pattern. We show that the transition is induced by suppression of the heterogeneous flux by spatial confinement. Systems with heterogeneous flux are ubiquitous; the effect is expected to be relevant to a wide variety of non-equilibrium processes under the action of spatial confinement.

scholarly journals Finite size corrections in two dimensional gauge theories and a quantitative chiral test of the overlap

1997 ◽  
Vol 399 (1-2) ◽  
pp. 105-112 ◽  
Author(s):  
Yoshio Kikukawa ◽  
Rajamani Narayanan ◽  
Herbert Neuberger
Keyword(s):  
Gauge Theories ◽  
Finite Size ◽  
Two Dimensional ◽  
Finite Size Corrections

FINITE-SIZE CORRECTIONS TO CORRELATION FUNCTION AND SUSCEPTIBILITY IN 2D ISING MODEL

2006 ◽  
Vol 17 (08) ◽  
pp. 1095-1105 ◽  
Author(s):  
J. KAUPUŽS
Keyword(s):  
Correlation Function ◽  
Ising Model ◽  
Correction Term ◽  
Finite Size ◽  
Scaling Exponent ◽  
Corrections To Scaling ◽  
Perfect Agreement ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Correction To Scaling

Transfer matrix calculations of the critical two-point correlation function in 2D Ising model on a finite-size [Formula: see text] lattice with periodic boundaries along 〈11〉 direction are extended to L = 21. A refined analysis of the correlation function in 〈10〉 crystallographic direction at the distance r = L indicates the existence of a nontrivial finite-size correction of a very small amplitude with correction-to-scaling exponent ω < 2 in agreement with our foregoing study for L ≤ 20. Here we provide an additional evidence and show that amplitude a of the multiplicative correction term 1 + aL-ω is about -3.5·10-8 if ω = 1/4 (the expected value). We calculate also the susceptibility for L ≤ 18 in order to compare our numerical estimates for the constant background contribution with the known very precise value and to look for possible nontrivial corrections to scaling. The numerical analysis reveals a perfect agreement for the background term, as well as shows that the nontrivial correction term, detected by our analysis in the correlation function, likely cancels in the susceptibility.

The partial realization theory of finite size two-dimensional arrays

1981 ◽  
Vol 64 (10) ◽  
pp. 1-8
Author(s):  
Tsuyoshi Matsuo ◽  
Yasumichi Hasegawa ◽  
Yoshikuni Okada
Keyword(s):  
Finite Size ◽  
Two Dimensional ◽  
Realization Theory

Smectic a1 ↔ a2 transition of n_c-60.8 : a two-dimensional phase separation of the molecular endgroups

1989 ◽  
Vol 50 (3) ◽  
pp. 375-385 ◽  
Author(s):  
H. Fadel ◽  
D. Guillon ◽  
A. Skoulios ◽  
F. Barbarin ◽  
M. Dugay
Keyword(s):  
Phase Separation ◽  
Two Dimensional
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