scholarly journals Universality and Exact Finite-Size Corrections for Spanning Trees on Cobweb and Fan Networks

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 895
Author(s):  
Nickolay Izmailian ◽  
Ralph Kenna
Keyword(s):  
Generating Functions ◽  
Spanning Trees ◽  
Central Charge ◽  
Finite Size ◽  
Universality Class ◽  
Partition Functions ◽  
Free Energies ◽  
Conformal Theory ◽  
Alternative Means ◽  
The Individual

The concept of universality is a cornerstone of theories of critical phenomena. It is very well understood in most systems, especially in the thermodynamic limit. Finite-size systems present additional challenges. Even in low dimensions, universality of the edge and corner contributions to free energies and response functions is less investigated and less well understood. In particular, the question arises of how universality is maintained in correction-to-scaling in systems of the same universality class but with very different corner geometries. Two-dimensional geometries deliver the simplest such examples that can be constructed with and without corners. To investigate how the presence and absence of corners manifest universality, we analyze the spanning tree generating function on two different finite systems, namely the cobweb and fan networks. The corner free energies of these configurations have stimulated significant interest precisely because of expectations regarding their universal properties and we address how this can be delivered given that the finite-size cobweb has no corners while the fan has four. To answer, we appeal to the Ivashkevich–Izmailian–Hu approach which unifies the generating functions of distinct networks in terms of a single partition function with twisted boundary conditions. This unified approach shows that the contributions to the individual corner free energies of the fan network sum to zero so that it precisely matches that of the web. It therefore also matches conformal theory (in which the central charge is found to be c = − 2 ) and finite-size scaling predictions. Correspondence in each case with results established by alternative means for both networks verifies the soundness of the Ivashkevich–Izmailian–Hu algorithm. Its broad range of usefulness is demonstrated by its application to hitherto unsolved problems—namely the exact asymptotic expansions of the logarithms of the generating functions and the conformal partition functions for fan and cobweb geometries. We also investigate strip geometries, again confirming the predictions of conformal field theory. Thus, the resolution of a universality puzzle demonstrates the power of the algorithm and opens up new applications in the future.

scholarly journals Exact finite-size corrections and corner free energies for the c=−2 universality class

2014 ◽  
Vol 884 ◽  
pp. 157-171 ◽  
Author(s):  
Nickolay Izmailian ◽  
Ralph Kenna ◽  
Wenan Guo ◽  
Xintian Wu
Keyword(s):  
Finite Size ◽  
Universality Class ◽  
Free Energies ◽  
Finite Size Corrections

CONFORMAL THEORY FOR YANG–LEE SINGULARITY OF 2D 3-STATE POTTS MODEL

2005 ◽  
Vol 19 (18) ◽  
pp. 3021-3035 ◽  
Author(s):  
TOMASZ WYDRO ◽  
JOHN F. McCABE
Keyword(s):  
Field Theory ◽  
Potts Model ◽  
Finite Size ◽  
Universality Class ◽  
Ising Models ◽  
Finite Size Scaling ◽  
Minimal Models ◽  
Edge Singularity ◽  
Conformal Theory ◽  
Conformal Field

We identify a conformal field theory (CFT) that describes the Yang–Lee edge singularity of the 2-dimensional (2D) 3-state Potts model. The identification is based on a comparison of finite-size scaling measurements to predictions for conformal minimal models. The comparison shows that the Yang–Lee edge singularities of the 2D 3-state Potts and the 2D Ising models are in the same universality class.

scholarly journals NON-HERMITIAN TRICRITICALITY IN THE BLUME-CAPEL MODEL WITH IMAGINARY FIELD

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3507-3529 ◽  
Author(s):  
G. VON GEHLEN
Keyword(s):  
Central Charge ◽  
Energy Levels ◽  
Finite Size ◽  
State Level ◽  
Universality Class ◽  
High Temperature Phase ◽  
Good Evidence ◽  
Spin Model ◽  
Temperature Phase ◽  
Imaginary Field

Using finite-size-scaling methods, we study the quantum chain version of the spin-1-Blume-Capel model coupled to an imaginary field. The aim is to realize simple non-unitary minimal conformal field theories in an Ising-type spin model. We find that the first ground-state level crossing in the high-temperature phase leads to a second-order phase transition of the Yang-Lee universality class (central charge c=−22/5). The Yang-Lee transition region ends at a line of a new type of tricriticality, where the three lowest energy levels become degenerate. The analysis of the spectrum at two points on this line gives good evidence that this line realizes the universality class of the ℳ2,7-conformal theory with c=−68/7.

scholarly journals Magnetic properties of CrFeCoNi based high entory alloy

2021 ◽  
Vol 2122 (1) ◽  
pp. 012004
Author(s):  
Junqi Yin ◽  
Markus Eisenbach ◽  
Makrus Daene ◽  
G. Malcolm Stocks
Keyword(s):  
Transition Temperature ◽  
Magnetic Order ◽  
Magnetic Phase ◽  
Finite Size ◽  
Exchange Interactions ◽  
Universality Class ◽  
Potential Approximation ◽  
High Entropy ◽  
Scaling Analyses ◽  
The Individual

Abstract Monte Carlo simulations are performed on three high entropy alloys: Cr0.25Fe0.25Co0.25Ni0.25, Cr0.2Fe0.2Co0.2Ni0.2Pd0.2, and Cr0.2Mn0.2Fe0.2Co0.2Ni0.2, with exchange interactions extracted from The ab initio Korringa-Kohn-Rostoker method combined with the coherent potential approximation calculations. Using finite size scaling analyses, we estimate the magnetic phase transition temperature for the four component alloy to be 108(2) K, and although the individual critical exponents are different from 3D Heisenberg universality class, the reduced exponent follows Suzuki weak universality. With the additional Palladium component, the transition temperature elevates to about 200 K. In contrast, we find no magnetic order for the five component alloy with Manganese at any finite temperatures.

Stabilization of Organic Carbon and Nitrogen in Consolidating Benthal Deposits

1985 ◽  
Vol 17 (6-7) ◽  
pp. 929-940 ◽  
Author(s):  
C. W. Bryant ◽  
L. G. Rich
Keyword(s):  
Organic Carbon ◽  
Model Verification ◽  
Volatile Acid ◽  
Free Energies ◽  
Organic Loading ◽  
Carbon And Nitrogen ◽  
Loading Rates ◽  
Degradation Reactions ◽  
The Individual ◽  
Organic Deposits

The objective of this research was to develop and validate a predictive model of the benthal stabilization of organic carbon and nitrogen in deposits of waste activated sludge solids formed at the bottom of an aerated water column, under conditions of continual deposition. A benthal model was developed from a one-dimensional, generalized transport equation and a set of first-order biological reactions. For model verification, depth profiles of the major interstitial carbon and nitrogen components were measured from a set of deposits formed in the laboratory at 20°C and a controlled loading rate. The observed sequence of volatile acid utilization in each benthal deposit was that which would be predicted by the Gibbs free energies of the individual degradation reactions and would be controlled by the reduction in interstitial hydrogen partial pressure with time. Biodegradable solids were solubilized rapidly during the first three weeks of benthal retention, but subsequent solubilization occurred much more slowly. The benthal simulation effectively predicted the dynamics of consolidating, organic deposits. Simulation of organic loading rates up to 250 g BVSS/(m2 day) indicated that the stabilization capacity of benthal deposits was far above the range of organic loading rates currently used in lagoon design.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

TRANSFER-MATRIX STUDY OF NEGATIVE-FUGACITY SINGULARITY OF HARD-CORE LATTICE GAS

1999 ◽  
Vol 10 (04) ◽  
pp. 517-529 ◽  
Author(s):  
SYNGE TODO
Keyword(s):  
Large Scale ◽  
Lattice Gas ◽  
Central Charge ◽  
Hard Core ◽  
Universality Class ◽  
Two Dimensions ◽  
Square Lattice ◽  
Lattice Gas Models ◽  
Renormalization Technique ◽  
Phenomenological Renormalization

A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point [Formula: see text] and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension xσ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.

Pyrolysis of Methane to Higher Hydrocarbons: A Thermodynamic Study

1989 ◽  
Vol 42 (10) ◽  
pp. 1655 ◽  
Author(s):  
FP Larkins ◽  
AZ Khan
Keyword(s):  
Gas Phase ◽  
Pressure Range ◽  
Solid Carbon ◽  
Free Energies ◽  
Oxidation Of Methane ◽  
Conversion Of Methane ◽  
Equilibrium Conversion ◽  
Benzene Toluene ◽  
Higher Hydrocarbons ◽  
The Individual

Some basic thermodynamic parameters such as Gibbs free energies, enthalpies of reactions and equilibrium compositions of products from the pyrolysis and partial oxidation of methane to higher hydrocarbons in the gas phase have been determined within a consistent framework for the temperature range 800-1500 K and the pressure range 0.1-3 MPa , by using the CSIRO-SGTE THERMODATA system. It has been established that the pyrolysis of methane to higher hydrocarbons, e.g. acetylene, ethylene, ethane, prop-1-ene, propane, benzene, toluene, naphthalene, 1-methylnaphthalene and 2-methylnaphthalene, considered as separate reactions, is a highly endothermic reaction with the Gibbs free energies for the individual reactions being positive until 1300 K. The aromatics are thermodynamically most favoured with the equilibrium yields increasing with temperature. Addition of O2 lowers the heats of synthesis and the free energies for methane conversion but no enhancement in the equilibrium yields of hydrocarbons is observed. When solid carbon is allowed, it is the dominant product in all cases with the equilibrium yields for all hydrocarbons becoming negligible. Increasing the pressure at a particular temperature has more effect on the lowering of the equilibrium conversion of methane than on the suppression of solid carbon. Such data are valuable for understanding the conversion limits for methane into higher hydrocarbons.

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