Lattice integrals of motion of the Ising model on the cylinder

We consider the 2D critical Ising model with spatially periodic boundary conditions. It is shown that for a suitable reparameterization of the known Boltzmann weights the transfer matrix becomes a polynomial in the variable csc(4u)$csc\left(4u\right)$, u$u$ being the spectral parameter. The coefficients of this polynomial are decomposed on the periodic Temperley–Lieb algebra by introducing a lattice version of the local integrals of motion.     

Static potentials for quarkonia at finite temperatures

We review non-perturbative static potentials commonly used in potential models for quarkonia at finite T. Potentials derived from Polyakov loop correlators are shown to be inappropriate for this purpose. The free energy is physical but has the wrong spatial decay and perturbative limit. The so-called singlet free energy is gauge dependent and unphysical. An appropriate static real time potential can be defined through a generalisation of pNRQCD to finite T. In perturbation theory, its real part reproduces the Debye-screened potential, its imaginary part accounts for Landau damping. Possibilities for its non-perturbative evaluation are discussed.     

Boundary States and Correlation Functions of Tricritical Ising Model from Coulomb-Gas Formalism

We consider the minimal conformaJ model describing the tricritical Ising model on the disk and on the upper half plane. Using the coulomb-gas formalism we determine its consistents boundary states as well as its one-point and two-point correlation functions.     

Absence of tricritical behavior of the random field Ising model in a honyecomb lattice

In this letter, we study the behavior of the random field Ising model on a honeycomb lattice by means of the effective field theory. We obtain the phase diagram in the T$T$–H$H$ plane for clusters with one spin in a finite size cluster scheme and it is observed the absence of a tricritical point.     

Two complex problems on the lattice: transport coefficients and finite chemical potential

After a few remarks about the problem of extracting transport coefficients from lattice QCD calculations, I report on recent developments in applying stochastic quantization and complex Langevin dynamics to field theories with a complex action due to a nonzero chemical potential. First results demonstrate that the sign problem poses no obstacle for this approach, even in the thermodynamic limit. I conclude with a comparison of two simple one-link models, describing a euclidean system at finite chemical potential and a Minkowski system in real time.     

Computer simulation study of a two-dimensional dipolar lattice

Summary The present work reports Monte Carlo calculations on a classical square lattice, consisting of purely dipolar plane rotators with identical dipole moments. Dipolar interactions are known not be essential for nematic ordering, but they can play a significant role in some specific cases; along the lines of the lattice model approximation already used in simulation work on liquid crystals, our system can be considered as an extreme case of nematogenic potential model. The system possesses an antiferroelectric ground state and, at higher temperature, it undergoes a transition to an orientationally disordered phase; comparison with the mean-field treatment of the transition is also reported. The structural properties were investigated by calculating orientational correlation functions, and found to exhibit some qualitative differences with respect to other potential models previously investigated for nematics. Simulation results indicate a close qualitative similarity with a three-dimensional analogue investigated in our previous work.

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Riassunto Il presente lavoro riporta calcoli Monte Carlo per un reticolo classico quadrato, costituito da rotatori piani puramente dipolari, con identici momenti. è noto che le interazioni dipolari non sono essenziali per l'ordinamento nematico, ma esse possono avere un ruolo significativo in alcuni casi specifici; lungo le linee dell'approssimazione a modello reticolare già applicata in lavori di simulazione per cristalli liquidi, il nostro sistema può pertanto venire considerato come un caso estremo di modello di potenziale nematogenico. Il sistema possiede stato fondamentale antiferroelettrico ed, a temperatura piú elevata, transisce ad una fase orientazionalmente disordinata; si riportano per confronto i risultati della trattazione a campo medio per tale transizione. Le proprietà strutturali furono investigate calcolando funzioni di correlazione orientazionale, e si è trovato che esse mostrano qualche differenza qualitativa rispetto ad altri modelli di potenziale previamente studiati per nematici. I risultati di simulazione indicano una stretta somiglianza qualitativa con un analogo tridimensionale investigato in nostri precedenti lavori.

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Резюме В этой работе предлагаются вычисления по методу Монте-Карло для классической квадратичной решетки, состоящей нз чнсто дипольных плоских ротаторов с тождественными дипольными моментами. Известно, что дипольные взаимодействия не являются существенными для нематического упорядочения, но они могут играть существенную роль в некоторых специфических случаях: в частности, в приближении модельной решетки, уже использованном при моделировании на жидких кристаллах, наша система может рассматриваться как предельный случай модели немтическочо потенциала. Рассмотренная система обладает антиферромагнитным основным состоянием и при высоких температурах она претерпевает переход в ориентационно разупорядоченную фазу; также проводится сравнение с рассмотрением этого перехода с помощью среднего поля. Исследуются структурные свойства, вычисляя ориентационные корреляционные функции. Обнаружено существование некоторых качественных различий по сравнению с моделями потенциалов, ранее использованных для нематиков. Результаты моделирования обнаруживают качественное подобие с трехмерным аналогом, исследованным в нашей предыдущей работе.

     

Computer simulation study of a simple cubic dipolar lattice

Summary The present work reports Monte Carlo calculations on a classical simple cubic lattice, consisting of point dipoles with identical dipole moments. Dipolar interactions are known not to be essential for nematic ordering, but they can play a significant role in some specific cases; along the lines of the lattice model approximation already used in simulation work on liquid crystals, our system can thus be considered as an extreme case of nematogenic potential model. The system possesses an antiferroelectric ground state and, at higher temperature, it undergoes a transition to an orientationally disordered phase; comparison with mean-field and spherical-model treatments of the transition is also reported. The structural properties were investigated by calculating orientational correlation functions and found to exhibit some qualitative differences with respect to other potential models previously investigated for nematics.

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Riassunto Il presente lavoro riporta calcoli Monte Carlo per un reticolo classico cubico semplice, costituito da dipoli puntiformi con identico momento dipolare. è noto che le interazioni dipolari non sono essenziali per l’ordinamento nematico, ma esse possono avere un ruolo significantivo in alcuni casi specifici; lungo le linee dell’approssimazione a modello reticolare già applicata in lavori di simulazione per cristalli liquidi, il nostro sistema può pertanto essere considerato come un caso estremo di modello di potenziale nematogenico. Il sistema possiede stato fondamentale antiferroelectrico ed, a temperature piú elevata, transisce ad una fase orientazionalmente disordinata; sono riportati per confronto i risultati delle trattazioni a campo medio, ed a modello sferico per tale transizione. Le proprietà strutturali furono investigate calcolando funzioni di correlazione orientazionale, e si è trovato che esse mostrano qualche differenza qualitativa rispetto ad altri modelli di potenziale previamente studiati per nematici.

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Резюме В работе предлагается моделирование по методу Монте-Карло классической простой кубической решетки, образованной точечными диполями с тождественными дипольными моментами. Известно, что дипольные взаимодействия не являются существенными для нематическояо упорядочения, но они игроют существенную роль в некоторых специфических случаях. Рассматриваемая система обладает антиферроэлектрическим основным состоянием и, при высокой темлературе, претерпевает переход в ориентационно упорядоченную фазу. Проводится сравнение с приближ=yeнием среднего поля и рассмотрением в рамках сферической модели этого перехода. Псследуутся структурные свойства, посредством вычисления ориентационных корреляционных функций. Обнаружены нектторые ксчественные различия по сравнению с другими потенциалыми моделями, ранее рассмотренными для описания нематики.

     

Relaxation times in a finite Ising system with random impurities

Finite-size scaling effects of the Ising model with quenched random impurities are studied, focusing on critical dynamics. In contrast to the pure Ising model, disordered systems are characterized by continuous relaxation time spectra. Dynamic field theory is applied to compute the spectral densities of the magnetizationM(t) and ofM ²(t). In addition, universal cumulant ratios are calculated to second order in ^1/4, where =4–d andd<4 denotes the spatial dimension.     

Span distribution moments for a symmetric one-dimensional random walk

Summary An easy derivation for the asymptotic behaviour of all the moments of the exact distribution of the distinct sites visited in a one-dimensional random walk is given. Comparison with numerical results is made.

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Riassunto Si ricavano gli andamenti asintotici di tutti i momenti della distribuzione esatta dei distinti siti visitati in un random walk unidimensionale. Gli stessi sono confrontati con risultati numerici.

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Резюме Предлогается простой вывод для асимптотического поведения всех моментов точного распределения для одномерного случайного блуждания. Проводится сравнение с численными результатами.

     

DNA denaturation for a tangled chain

Summary We have considered a model of a lattice gas defined on a periodic tangled chain to study the DNA denaturation by a modified transfer matrix method. By using an iterative algorithm we have obtained numerically different kinds of melting curves for different configurations of the tangled chain and different types of interactions. In some special cases of configurations and interactions we have found the same melting curves, which we have obtained before studying some simple lattice gas models, using different techniques. This more generalized model and the new results could be useful for the experimental investigations.     

QCD thermodynamics at zero and non-zero density

We present results on the QCD equation of state, obtained with two different improved dynamical staggered fermion actions and almost physical quark masses. Lattice cut-off effects are discussed in detail as results for three different lattice spacings are available now, i.e. results have been obtained on lattices with temporal extent of N_τ = 4, 6 and 8. Furthermore we discuss the Taylor expansion approach to non-zero baryon chemical potential by means of an expansion of the pressure. We use the expansion coefficients to calculate various fluctuations and correlations among hadronic charges. We find that the correlations reproduce the qualitative behavior of the resonance gas model below T_c and start to agree with the free gas predictions for T1.5T_c.     

On one-point functions for sinh-Gordon model at finite temperature

Using fermionic basis we conjecture the exact formulae for the expectation values of local fields in sinh-Gordon model. The conjecture is checked against previously known results.     

Phase diagrams in an ultra-thin spin-1 transverse Ising film with bond or site dilution at surfaces

The phase diagrams of two nanoscaled thin films with bond and site dilutions at the surfaces, described by the spin-1 transverse Ising model, are investigated by the use of an effective field theory with correlations. A number of characteristic phenomena have been found in them, which are heavily dependent on the ratios (r = J₁/J and p = Ω_S/Ω, where J is the exchange interaction in the inner layer, J₁ is the exchange interaction between the surface and the next inner layer, Ω_S is the transverse field at the surfaces and Ω is the transverse field in the inner layer). Some of them have exhibited very similar behaviors found in the two spin-1/2 nanoscaled thin films with bond and site dilutions at the surfaces.     

An Improved Heterogeneous Mean-Field Theory for the Ising Model on Complex Networks

Heterogeneous mean-field theory is commonly used methodology to study dynamical processes on complex networks,such as epidemic spreading and phase transitions in spin models.In this paper,we propose an improved heterogeneous mean-field theory for studying the Ising model on complex networks.Our method shows a more accurate prediction in the critical temperature of the Ising model than the previous heterogeneous mean-field theory.The theoretical results are validated by extensive Monte Carlo simulations in various types of networks.     

On the mean-field Ising model in a random external field

We use a method developed by van Hemmen to obtain the free energy of the mean-field Ising model in a random external magnetic field. Some results of previous mean-field calculations are confirmed and generalized. The tricritical point in the global phase diagram is discussed in detail. We also consider different probability distributions of the random fields and provide some proofs regarding the conditions for the existence of a tricritical point.     

The Roper resonance in a finite volume

We calculate the energy levels corresponding to the Roper resonance based on a two-flavor chiral effective Lagrangian for pions, nucleons, deltas, and the Roper resonance at the leading one-loop order. We show that the Roper mass can be extracted from these levels for lattice volumes of moderate size.     

Phase diagrams of the transverse Ising antiferromagnet in the presence of the longitudinal magnetic field

In this paper we study the critical behavior of the two-dimensional antiferromagnetic Ising model in both uniform longitudinal (H$H$) and transverse (Ω$\Omega$) magnetic fields. Using the effective-field theory (EFT) with correlation in single site clusters we calculate the phase diagrams in the H−T$H-T$ and Ω−T$\Omega -T$ planes for the square lattice. We have only found second order phase transitions for all values of fields and reentrant behavior was not observed.     

Solvable models of classical lattice gases

We study classical lattice gases at fixed temperature but variable fugacity. It is shown how the thermodynamic functions may be calculated exactly provided the Boltzmann weights are representable as principal minors of a convolution operator. We explicitly construct this operator for the cluster models of Fisher and Felderhof.On leave from the Institute for Theoritical Physics, RWTH Aachen, Germany.