scholarly journals Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Victor Gorbenko ◽  
Slava Rychkov ◽  
Bernardo Zan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Fixed Points ◽  
Potts Model ◽  
General Relation ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Minimal Models ◽  
The Real ◽  
First Order

We study complex CFTs describing fixed points of the two-dimensional QQ-state Potts model with Q≻ 4Q>4. Their existence is closely related to the weak first-order phase transition and the "walking" renormalization group (RG) behavior present in the real Potts model at Q𕣒Q>4. The Potts model, apart from its own significance, serves as an ideal playground for testing this very general relation. Cluster formulation provides nonperturbative definition for a continuous range of parameter QQ, while Coulomb gas description and connection to minimal models provide some conformal data of the complex CFTs. We use one and two-loop conformal perturbation theory around complex CFTs to compute various properties of the real walking RG flow. These properties, such as drifting scaling dimensions, appear to be common features of the QFTs with walking RG flows, and can serve as a smoking gun for detecting walking in Monte Carlo simulations.The complex CFTs discussed in this work are perfectly well defined, and can in principle be seen in Monte Carlo simulations with complexified coupling constants. In particular, we predict a pair of S_5S5-symmetric complex CFTs with central charges c\approx 1.138 \pm 0.021 ic≈1.138±0.021i describing the fixed points of a 5-state dilute Potts model with complexified temperature and vacancy fugacity.

FIRST-ORDER TRANSITION, FINITE-ISOLATED SYSTEM AND MICROCANONICAL MONTE CARLO SIMULATIONS

2002 ◽  
Vol 16 (24) ◽  
pp. 3567-3572 ◽  
Author(s):  
SMITA OTA ◽  
SNEHADRI BIHARI OTA
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Spin Model ◽  
Order Transition ◽  
Microcanonical Ensemble ◽  
Two Dimensional ◽  
First Order ◽  
Equilibrium Response ◽  
First Order Transition

We have investigated the first-order transition in the classical two-dimensional (2D) extended XY-spin model using Monte Carlo simulations. The simulations have been carried out on a system with 100 spins in the microcanonical ensemble, which represents a finite-isolated system. The energy as a function of temperature is found to exhibit a 'S'-shape at the first-order transition. We conclude that the observed phenomena at the first-order transition should be interpreted as the equilibrium response of a finite-isolated system.

ON THE CALCULATION OF THE HEAT CAPACITY IN PATH INTEGRAL MONTE CARLO SIMULATIONS

1992 ◽  
Vol 03 (02) ◽  
pp. 337-346 ◽  
Author(s):  
D. MARX ◽  
P. NIELABA ◽  
K. BINDER
Keyword(s):  
Heat Capacity ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Path Integral ◽  
General Relation ◽  
Absolute Magnitude ◽  
Computational Effort ◽  
Imaginary Time ◽  
Time Dimension ◽  
Path Integral Monte Carlo

In Path Integral Monte Carlo simulations the systems partition function is mapped to an equivalent classical one at the expense of a temperature-dependent Hamiltonian with an additional imaginary time dimension. As a consequence the standard relation linking the heat capacity Cv to the energy fluctuations, <E2>−<E>2, which is useful in standard classical problems with temperature-independent Hamiltonian, becomes invalid. Instead, it gets replaced by the general relation [Formula: see text] for the intensive heat capacity estimator; β being the inverse temperature and the subscript P indicates the P-fold discretization in the imaginary time direction. This heatcapacity estimator has the advantage of being based directly on the energy estimatorand thus requires no extra computational effort and is suited for extensive phase diagramstudies. As an example, numerical results are presented for a two-dimensional fluid withinternal magnetic quantum degrees of freedom. We discuss in detail origin and consequences of the excess term. Due to the subtraction of two relatively large contributions ofsimilar absolute magnitude a large statistical effort would be necessary for very accurateheat capacity estimates.

Percolation in two-dimensional quasicrystals by Monte Carlo simulations

1989 ◽  
Vol 22 (14) ◽  
pp. L705-L709 ◽  
Author(s):  
S Sakamoto ◽  
F Yonezawa ◽  
K Aoki ◽  
S Nose ◽  
M Hori
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Two Dimensional

An Equilibrium Prediction Method for Control and Fault Detection of Energy Systems

2021 ◽  
Author(s):  
Austin Rogers ◽  
Fangzhou Guo ◽  
Bryan Rasmussen
Keyword(s):  
Monte Carlo ◽  
Fault Detection ◽  
Monte Carlo Simulations ◽  
Case Studies ◽  
Air Conditioning ◽  
Prediction Method ◽  
Worker Safety ◽  
Static System ◽  
Control Logic ◽  
First Order

Abstract Many fault detection, optimization, and control logic methods rely on sensor feedback that assumes the system is operating at steady state conditions, despite persistent transient disturbances. While filtering and signal processing techniques can eliminate some transient effects, this paper proposes an equilibrium prediction method for first order dynamic systems using an exponential regression. This method is particularly valuable for many commercial and industrial energy system, whose dynamics are dominated by first order thermo-fluid effects. To illustrate the basic advantages of the proposed approach, Monte Carlo simulations are used. This is followed by three distinct experimental case studies to demonstrate the practical efficacy of the proposed method. First, the ability to predict the carbon dioxide level in classrooms allows for energy efficient control of the ventilation system and ensures occupant comfort. Second, predicting the optimal time to end the cool-down of an industrial sintering furnace allows for maximum part throughput and worker safety. Finally, fault detection and diagnosis methods for air conditioning systems typically use static system models; however, the transient response of many air conditioning signals may be approximated as first order, and therefore, the prediction model enables the use of static fault detection methods with transient data. In this paper, the equilibrium prediction method's performance will be quantified using both Monte Carlo simulations and case studies.

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