Finite lattice systems with true critical behavior

1992 ◽  
Vol 46 (4) ◽  
pp. 1643-1657 ◽  
Author(s):  
J. L. deLyra ◽  
S. K. Foong ◽  
T. E. Gallivan
Keyword(s):  
Critical Behavior ◽  
Finite Lattice ◽  
Lattice Systems

Obtaining sharp critical behavior in finite lattice systems

1992 ◽  
Vol 26 ◽  
pp. 601-603
Author(s):  
J.L. deLyra ◽  
S.K. Foong ◽  
T.E. Gallivan
Keyword(s):  
Critical Behavior ◽  
Finite Lattice ◽  
Lattice Systems

Bond percolation on a finite lattice: Critical behavior of the (1+ε)-state Potts model

1994 ◽  
Vol 49 (2) ◽  
pp. 1016-1025 ◽  
Author(s):  
Joseph Rudnick ◽  
Jacob Morris ◽  
George Gaspari
Keyword(s):  
Critical Behavior ◽  
Potts Model ◽  
Finite Lattice ◽  
Bond Percolation

scholarly journals Critical behavior in active lattice models of motility-induced phase separation

2021 ◽  
Vol 44 (4) ◽  
Author(s):  
Florian Dittrich ◽  
Thomas Speck ◽  
Peter Virnau
Keyword(s):  
Phase Separation ◽  
Critical Behavior ◽  
Rotational Diffusion ◽  
Lattice Models ◽  
Universality Class ◽  
Computationally Efficient ◽  
Lattice Systems ◽  
Active Particles ◽  
Open Question

Abstract Lattice models allow for a computationally efficient investigation of motility-induced phase separation (MIPS) compared to off-lattice systems. Simulations are less demanding, and thus, bigger systems can be accessed with higher accuracy and better statistics. In equilibrium, lattice and off-lattice models with comparable interactions belong to the same universality class. Whether concepts of universality also hold for active particles is still a controversial and open question. Here, we examine two recently proposed active lattice systems that undergo MIPS and investigate numerically their critical behavior. In particular, we examine the claim that these systems and MIPS in general belong to the Ising universality class. We also take a more detailed look on the influence and role of rotational diffusion and active velocity in these systems. Graphic Abstract

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Elastic scattering from cubic lattice systems with paracrystalline distortion. II

1990 ◽  
Vol 41 (6) ◽  
pp. 3854-3856 ◽  
Author(s):  
Hideki Matsuoka ◽  
Hideaki Tanaka ◽  
Norio Iizuka ◽  
Takeji Hashimoto ◽  
Norio Ise
Keyword(s):  
Elastic Scattering ◽  
Lattice Systems ◽  
Cubic Lattice
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