Infinite-Cutoff Renormalization of the Chiral Nucleon–Nucleon Interaction up to N3LO

Naively, the “best” method of renormalization is the one where a momentum cutoff is taken to infinity while maintaining stable results due to a cutoff-dependent adjustment of counterterms. We have applied this renormalization method in the non-perturbative calculation of phase-shifts for nucleon–nucleon (NN) scattering using chiral NN potentials up to next-to-next-to-next-to-leading order (N³LO). For lower partial waves, we find that there is either no convergence with increasing order or, if convergence occurs, the results do not always converge to the empirical values. For higher partial waves, we always observe convergence to the empirical phase shifts (except for the ³G₅ state). Furthermore, no matter what the order is, one can use only one or no counterterm per partial wave, creating a rather erratic scheme of power counting that does not allow for a systematic order-by-order improvement of the predictions. The conclusion is that infinite-cutoff renormalization is inappropriate for chiral NN interactions, which should not come as a surprise, since the chiral effective field theory (chiral EFT), these interactions are based upon, is designed for momenta below the chiral-symmetry breaking scale of about 1 GeV. Therefore, this value for the hard scale should also be perceived as the appropriate upper limit for the momentum cutoff.     

Fluctuation interaction of Ising subsystems

A phase diagram of two Ising subsystems σ and s has been constructed on a Bethe lattice with a coordination number 4 (a simplified analog of a square lattice). In contrast to the known Ashkin-Teller model, the interaction between these two subsystems is of a purely fluctuational nature; i.e., it does not manifest itself in the ground state and nullifies the sums of the products of average spins 〈σ〉〈s〉 (interactions of this type are realized in lattice-type adsorbed systems with dipolelike intermolecular interactions and strong azimuthal angular dependence of the adsorption potential of symmetry C₄). Apart from conventional states, i.e., a high-temperature disordered state (〈σ〉=〈s〉=0) and a low-temperature ordered state (〈σ〉 and 〈s〉 =? 0), this system can also exist in a correlated state (〈σs〉 =? 0 at 〈σ〉=〈s〉=0). In the theory of orientational phase transitions, this state corresponds to a fundamentally different, intermediate (on the temperature axis) phase in which a preferred direction of long molecule axes arises in the absence of spontaneous polarization. The results of Monte Carlo simulation on a square lattice agree with the conclusions obtained on a Bethe lattice. The characteristics of the orientational phase transition in a 2 × 1 monolayer of CO molecules adsorbed on the NaCl(100) surface are discussed.     

A Wilson-Yukawa Model with undoubled chiral fermions in 2D

We consider the fermion mass spectrum in the strong coupling vortex phase (VXS) of a lattice fermion-scalar model with a global U(1)_L × U(1)_R, in two dimensions, in the context of a recently proposed two-cutoff lattice formulation. The fermion doublers are made massive by a strong Wilson-Yukawa coupling, but in contrast with the standard formulation of these type of models, in which the light fermion spectrum was found to be vector-like, we find massless fermions with chiral quantum numbers at finite lattice spacing. When the global symmetry is gauged, this model is expected to give rise to a lattice chiral gauge theory.     

Critical behavior of the one-dimensional commensurate-incommensurate transition

We study the low-temperature critical behavior of one-dimensional charge-density-waves coupled to an underlying lattice, using the McMillan free energy. For weak coupling, the incommensurate CDW orders at T = 0 as a lattice of phase slip solutions with XY critical behavior. For strong coupling, the commensurate CDW orders at T = 0 with Ising critical behavior. Analytic expressions for the low-temperature inverse correlation length and average phase change are obtained for all values of the coupling to the lattice.     

Phase transitions and critical properties of the frustrated Heisenberg model on a layer triangular lattice with next-to-nearest-neighbor interactions

The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J ₁) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = |J ₁/J| = 0?C0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.     

Topological susceptibility in lattice QCD with unimproved Wilson fermions

We address a long standing problem regarding topology in lattice simulations of QCD with unimproved Wilson fermions. Earlier attempt with unimproved Wilson fermions at β=5.6 to verify the suppression of topological susceptibility with decreasing quark mass (mq) was unable to unambiguously confirm the suppression. We carry out systematic calculations for two degenerate flavours at two different lattice spacings (β=5.6 and 5.8). The effects of quark mass, lattice volume and the lattice spacing on the spanning of different topological sectors are presented. We unambiguously demonstrate the suppression of the topological susceptibility with decreasing quark mass, expected from chiral Ward identity and chiral perturbation theory.     

Phase Diagram and Structure of the Ground State of the Antiferromagnetic Ising Model on a Body-Centered Cubic Lattice

The Monte Carlo method has been used to study phase transitions and the structure of the ground state of the antiferromagnetic Ising model on a body-centered cubic lattice taking into account the interactions of nearest and next nearest neighbors. All possible magnetic structures of the ground state have been obtained for the first time as a function of the ratio of exchange interactions r. It is shown that six different orderings in the ground state are possible in the system as a function of the r value. The phase diagram of the dependence of the critical temperature on the interaction of the next nearest neighbors is constructed. For the first time, a narrow region (2/3 < r ≤ 0.75) is found in the diagram where the transition from the antiferromagnetic phase to the paramagnetic phase occurs as a first-order phase transition. It is shown that the competition between exchange interactions at the value r = 2/3 does not lead to the frustration and degeneracy of the ground state.     

Kurtosis and compressibility near the chiral phase transition

The properties of net quark number fluctuations in the vicinity of the QCD chiral phase transition are discussed in terms of an effective chiral model in the mean-field approximation. We focus on the ratio of the fourth- to second-order cumulants (kurtosis) and the compressibility of the system and discuss their dependence on the pion mass. It is shown that near the chiral phase transition, both observables are sensitive to the value of mπ$m_{\pi }$. For physical mπ$m_{\pi }$, the kurtosis exhibits a peak whereas the inverse compressibility shows a dip at the pseudocritical temperature. These structures disappear for large mπ$m_{\pi }$. Our results, obtained in an effective model with two flavors, are qualitatively consistent with recent results of 2+1$2+1$ flavor lattice gauge theory. We also discuss the high- and low-temperature properties of these observables and the role of the coupling of the quark degrees of freedom to the Polyakov loop.     

Disordered d-wave superconductors with interactions

We study the localization properties of disordered d-wave superconductors by means of the fermionic replica trick method. We derive the effective non-linear σ-model describing the diffusive modes related to spin transport which we analyze by the Wilson–Polyakov renormalization group. A lot of different symmetry classes are considered within the same framework. According to the presence or the absence of certain symmetries, we provide a detailed classification for the behavior of some physical quantities, like the density of states, the spin and the quasiparticle charge conductivities. Following the original Finkel'stein approach, we finally extend the effective functional method to include residual quasiparticle interactions, at all orders in the scattering amplitudes. We consider both the superconducting and the normal phase, with and without chiral symmetry, which occurs in the so-called two-sublattice models.     

Chiral phase transition in lattice QCD with Wilson quarks

The nature of the chiral phase transition in lattice QCD is studied for the cases of 2, 3 and 6 flavors with degenerate Wilson quarks, mainly on a lattice with the temporal direction extensionN _t=4. We find that the chiral phase transition is continuous for the case of 2 flavors, while it is of first order for 3 and 6 flavors.     

Chiral phase transition in lattice QCD with Wilson quarks

The nature of the chiral phase transition in lattice QCD is studied for the cases of 2, 3 and 6 flavors with degenerate Wilson quarks, mainly on a lattice with the temporal direction extensionN _t=4. We find that the chiral phase transition is continuous for the case of 2 flavors, while it is of first order for 3 and 6 flavors.     

Amplitudes of multichannel scattering on a two-dimensional potential barrier with constant height

The immersing method is applied to solve the N-channel scattering problem for concrete potential. In particular, we consider the particle scattering on a two-dimensional potential barrier, which is constant in the scattering direction and arbitrary in the cross-section direction. For this case the scattering amplitudes t _m and r _m (1,2, m= ...,N) are determined. A transition from the obtained formulas to the case of ?-potential is performed. For this case transmission amplitudes t _m and reflection amplitudes r _m are obtained. It is also shown that the product of transmission and reflection amplitudes along the channel m does not depend on the scattering channel.     

Magnetic phase diagram of a random mixture of Jahn-Teller ions

A magnetic model of a random mixture containing Jahn-Teller ions, in which several kinds of exchange interactions between the Jahn-Teller ions and between the Jahn-Teller and non-Jahn-Teller ions are assumed, is proposed and studied by using the distribution function method. It is shown that a spin glass phase occurs when these exchange interactions have different signs. Our model would be applicable to a mixture Rb₂Cr_xMn_1-xCl₄ in which the spin glass phase has been observed.     

Equilibrium properties of a spin-1 Ising system with bilinear,biquadratic and odd interactions

The equilibrium properties of the spin-1 Ising system Hamiltonian with arbitrary bilinear (J), biquadratic (K) and odd (L), which is also called dipolar-quadrupolar, interactions is studied for zero magnetic field in the lowest approximation of the cluster variation method. The odd interaction is combined with the bilinear (dipolar) and biquadratic (quadrupolar) exchange interactions by the geometric mean. In this system, phase transitions depend on the ratio of the coupling parameters, α = J/K; therefore, the dependence of the nature of the phase transition on α is investigated extensively and it is found that for α ⩽ 1 and α ⩾ 2000 a second-order phase transition occurs, and for 1 < α < 2000 a first-order phase transition occurs. The critical temperatures in the case of a second-order phase transition and the upper and lower limits of stability temperature in the case of a first-order phase transition are obtained for different values of α calculated using the Hessian determinant. The first-order phase transition temperatures are found by using the free energy values while increasing and decreasing the temperature. Besides the stable branches of the order parameters, we establish also the metastable and unstable parts of these curves and the thermal variations of these solutions as a function of the reduced temperature are investigated. The unstable solutions for the first-order phase transitions are obtained by displaying the free energy surfaces in the form of a contour map. Results are compared with the spin-1 Ising system Hamiltonian with the bilinear and biquadratic interactions and it is found that the odd interaction greatly influences the phase transitions.     

Phase transitions in the two-dimensional ferro- and antiferromagnetic potts models on a triangular lattice

The phase transitions in the two-dimensional ferro- and antiferromagnetic Potts models with q = 3 states of spin on a triangular lattice are studied using cluster algorithms and the classical Monte Carlo method. Systems with linear sizes L = 20–120 are considered. The method of fourth-order Binder cumulants and histogram analysis are used to discover that a second-order phase transition occurs in the ferromagnetic Potts model and a first-order phase transition takes place in the antiferromagnetic Potts model. The static critical indices of heat capacity (α), magnetic susceptibility (γ), magnetization (β), and correlation radius index (ν) are calculated for the ferromagnetic Potts model using the finite-size scaling theory.     

The extended quark sigma model at finite temperature and baryonic chemical potential

An extended quark sigma model which includes higher-order mesonic interactions is studied at the finite baryonic chemical potential u _B and temperature T. The field equations have been solved in the mean-field approximation by using the modified iteration method at finite baryonic chemical potential u _B and temperature T. The Goldstone theorem is satisfied below a critical temperature in the chiral limit for u _B = 0. As expected from general universality, the chiral phase transition is second-order. By including the higher-order mesonic interactions, the critical temperature is reduced compared to that found in recent works and is in good agreement with lattice QCD results. The nucleon mass is examined in the (u _B , T) plane, showing a strong dependence on u _B and T. We find that an increase in both the baryonic chemical potential u _B and the temperature T leads to an increase in the values of the nucleon mass. This is evidence for the quark-gluon deconfinement phase transition at higher values of temperature.     

The thermodynamics of SU(3) lattice gauge theory with a light isodoublet of quarks

Using hybrid differential equations with stochastic pseudo-fermion fields, we simulated SU(3) lattice gauge theory with a light isodoublet of quarks on a 4 × 8³ lattice. The bare quark mass is 0.0125 in lattice units which corresponds to 7.75 MeV if the finite temperature chiral transition occurs at T_c=155 MeV as suggested by phenomenology. The transition is first order and metastable states are found over a narrow range in temperature. Results for 4⁴ lattices are also presented for 2 and 3 light flavors.     

Orientational phase transitions in quadrupolar strands with itinerant-electrons

We consider a linear strand of chemically equivalent molecules of spin S = 1 which are free to rotate about their centres of mass fixed to a rigid lattice. The molecules interact via nearest-neighbour quadrupolar interactions and the electrons, occupying a half-filled, tight-binding conduction band, hop between nearest-neighbour molecules only. With a mean-field theory, we study the dependence of the metal-insulator phase transition temperature T_c on the quadrupole-quadrupole interaction, the electron-quadrupole interaction as well as the bandwidth of the conduction band.     

BKT phase transition in a 2D system with long-range dipole-dipole interaction

We consider phase transitions in 2D XY-like systems with long-range dipole-dipole interactions and demonstrate that BKT-type phase transition always occurs separating the ordered (ferroelectric) and the disordered (paraelectric) phases. The low-temperature phase corresponds to a thermal state with bound vortex-antivortex pairs characterized by linear attraction at large distances. Using the Maier-Schwabl topological charge model, we show that bound vortex pairs polarize and screen the vortex-antivortex interaction, leaving only the logarithmic attraction at sufficiently large separations between the vortices. At higher temperatures the pairs dissociate and the phase transition similar to BKT occurs, though at a larger temperature than in a system without the dipole-dipole interaction.     

Melting and wetting transitions in the three-state chiral clock model

The melting transition of the two-dimensional, three-state, asymmetric or chiral clock model is examined. Evidence from scaling arguments and analysis of perturbation series is presented, indicating that the chiral symmetry-breaking operator is relevant at the symmetric (or pure Potts) critical point with a crossover exponent of ø ≈ 0.2. The remainder of the commensurate-disordered phase boundary therefore appears to be in a new universality class, distinct from the pure three-state Potts transition. An interfacial wetting transition that plays an important role in the crossover between the two types of critical behavior is discussed. The location and exponents of this wetting transition are obtained both in a low-temperature limit using generating function techniques and in a systematic low-temperature expansion of the transfer matrix.