Ferromagnetic phase transition for the spanning-forest model (q-->0 limit of the Potts model) in three or more dimensions

We present Monte Carlo simulations of the spanning-forest model (q-->0 limit of the ferromagnetic Potts model) in spatial dimensions d=3, 4, 5. We show that, in contrast to the two-dimensional case, the model has a ferromagnetic second-order phase transition at a finite positive value w(c). We present numerical estimates of w(c) and of the thermal and magnetic critical exponents. We conjecture that the upper critical dimension is 6.     

Semiclassical theory of the Anderson transition

We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the critical disorder as a function of the spatial dimensionality d. The critical exponent nu controlling the divergence of the localization length at the transition is found to be nu=1/2+1/d-2 thus confirming that the upper critical dimension is infinity. Level statistics are investigated in detail. We show that the two level correlation function decays exponentially and the number variance is linear with a slope which is an increasing function of the spatial dimensionality. Our analytical findings are in agreement with previous numerical results.     

Mean field theory with correlations in space and time for the ferromagnetic phase transition

A mean field theory with correlations in space and time is proposed which implicitly takes into account the effect of thermal spin fluctuations. The theory describes the kinetic critical slowing down of the relaxation of the magnetization near the ferromagnetic phase transition in crystalline and amorphous ferromagnets. Furthermore, it provides an explanation for the large temperature range of apparent “critical” behaviour as observed experimentally for the paramagnetic susceptibility of amorphous ferromagnets.     

Anomalous scaling at the quantum critical point in itinerant antiferromagnets

We show that the Hertz phi(4) theory of quantum criticality is incomplete as it misses anomalous nonlocal contributions to the interaction vertices. For antiferromagnetic quantum transitions, we found that the theory is renormalizable only if the dynamical exponent z=2. The upper critical dimension is still d=4 - z=2; however, the number of marginal vertices at d=2 is infinite. As a result, the theory has a finite anomalous exponent already at the upper critical dimension. We show that for d<2 the Gaussian fixed point splits into two non-Gaussian fixed points. For both fixed points, the dynamical exponent remains z=2.     

Universality of synchrony: critical behavior in a discrete model of stochastic phase-coupled oscillators

We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a critical value. When coupling between units is strictly local, the model undergoes a continuous phase transition which we characterize numerically using finite-size scaling analysis. In particular, the onset of global synchrony is marked by signatures of the XY universality class, including the appropriate classical exponents beta and nu, a lower critical dimension d(lc) = 2, and an upper critical dimension d(uc) = 4.     

Ising gauge theory in 3.999… dimensions

We numerically study Ising gauge theories in non-integer dimensions below four dimensions using fractals. We find indications that the first-order transition of the d = 4 theory becomes second order for d = 4 − ϵ for arbitrarily small non-zero ϵ. This suggests that the upper critical dimension of abelian gauge theories is four.     

Magnetic and magnetocaloric results of magnetic field-induced transitions in La1−xCexMn2Si2 (x=0.35 and 0.45) compounds

The La_1−xCe_xMn₂Si₂ compounds (x=0.35 and 0.45) exhibit an antiferromagnetic-ferromagnetic transition caused by the changes in distance between Mn atoms due to temperature changes. A field-induced transition from antiferromagnetic state to ferromagnetic state at a critical field, which decreases with increase in temperature, can also be induced by applying a magnetic field. In this paper our aim is to study the magnetization and magnetocaloric effect, close to transition temperatures. Our subsidiary aim is to examine the temperature dependence of critical field and ferromagnetic fraction of compounds. The variation of magnetocaloric effect with temperature is correlated with the ferromagnetic-antiferromagnetic phase coexistence. Our final aim is to examine the harmony between magnetocaloric effect values calculated both by the Maxwell theory and by the Landau theory.     

Transient magnetostriction in ferro- and ferri-magnetic materials

An acoustic impulse excited by a laser pulse generates some transient magnetostriction effects in various ferromagnetic and ferrimagnetic materials. A crystal of small magnetic anisotropy energy gives a steady magnetoelastic oscillation which is resonant with the sample dimension. The other materials show the surface effect only. The temperature dependence is studied up to the Curie temperature. Around the phase transition point the long-wavelength fluctuation of magnetization is excited by the elastic impulse, and some critical phenomena are observed. These effects are discussed by the usual theory of magnetoelastic interaction.     

The fully finite spherical model

A lattice sum technique is applied to the constraint equation of the finite size mean spherical model. It is shown that this allows the investigation of the model over a wide range of temperatures, for a wide range of system sizes. Correlation lengths and susceptibilities are shown to obey crossover scaling aroundT=0 below the lower critical dimension, and finite size scaling between the lower and upper critical dimensions. Universal scaling forms are suggested for the lower critical dimension. At and above the upper critical dimension, the behavior is identical to that of finite sized mean field theory. The scaling at and above the upper critical dimension is shown to be modified by the existence of a dangerous irrelevant variable which also governs the failure of hyperscaling. Implications for phenomenological renormalization experiments are discussed. Numerical results of scaling are displayed.     

Random-field spin models beyond 1 loop: a mechanism for decreasing the lower critical dimension

The functional renormalization group for the random-field and random-anisotropy O(N) sigma models is studied to 2 loop. The ferromagnetic-disordered (F-D) transition fixed point is found to next order in d = 4 + epsilon for N > N(c) (N(c) = 2.834 740 8 for random field, N(c) = 9.441 21 for random anisotropy). For N < N(c) the lower critical dimension d = d(lc) plunges below d(lc) = 4: we find two fixed points, one describing the quasiordered phase, the other is novel and describes the F-D transition. d(lc) can be obtained in an (N(c)-N) expansion. The theory is also analyzed at large N and a glassy regime is found.     

Slow Motion and Metastability for a Nonlocal Evolution Equation

In this paper we consider a nonlocal evolution equation in one dimension, which describes the dynamics of a ferromagnetic system in the mean field approximation. In the presence of a small magnetic field, it admits two stationary and homogeneous solutions, representing the stable and metastable phases of the physical system. We prove the existence of an invariant, one dimensional manifold connecting the stable and metastable phases. This is the unstable manifold of a distinguished, spatially nonhomogeneous, stationary solution, called the critical droplet.^{(4, 10)} We show that the points on the manifold are droplets longer or shorter than the critical one, and that their motion is very slow in agreement with the theory of metastable patterns. We also obtain a new proof of the existence of the critical droplet, which is supplied with a local uniqueness result.     

Asymmetric metal-insulator transition in disordered ferromagnetic films

We present experimental data and a theoretical interpretation of the conductance near the metal-insulator transition in thin ferromagnetic Gd films of thickness b ≈ 2-10 nm. A large phase relaxation rate caused by scattering of quasiparticles off spin-wave excitations renders the dephasing length L(?) ? b in the range of sheet resistances considered, so that the effective dimension is d = 3. The conductivity data at different stages of disorder obey a fractional power-law temperature dependence and collapse onto two scaling curves for the metallic and insulating regimes, indicating an asymmetric metal-insulator transition with two distinctly different critical exponents; the best fit is obtained for a dynamical exponent z ≈ 2.5 and a correlation (localization) length critical exponent ν- ≈ 1.4 (ν+ ≈ 0.8) on the metallic (insulating) side.     

Universal scaling behavior at the upper critical dimension of nonequilibrium continuous phase transitions

In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of the upper critical dimension. We apply our method to a nonequilibrium continuous phase transition. By focusing on the equation of state of the phase transition it is easy to extend our analysis to all equilibrium and nonequilibrium phase transitions observed numerically or experimentally.     

Spontaneous spin polarization in doped semiconductor quantum wells

We calculate the critical density of the zero-temperature, first-order ferromagnetic phase transition in n-doped GaAs/AlGaAs quantum wells. We predict that this transition could be observed in narrow quantum wells at electron densities somewhat lower than the ones that have been considered experimentally thus far, and that there exists an upper limit for the well width beyond which there would be no transition as long as only one subband is populated. Our calculations are done within a screened Hartree-Fock approximation with a polarization-dependent effective mass, which is adjusted to match the critical density predicted by Monte Carlo calculations for the strictly two-dimensional electron gas.     

Quantum critical behavior of clean itinerant ferromagnets

We consider the quantum ferromagnetic transition at zero temperature in clean itinerant electron systems. We find that the Landau-Ginzburg-Wilson order parameter field theory breaks down since the electron-electron interaction leads to singular coupling constants in the Landau- Ginzburg-Wilson functional. These couplings generate an effective long-range interaction between the spin or order parameter fluctuations of the form 1 <r ² d?1, with d the spatial dimension. This leads to unusual scaling behavior at the quantum critical point in 1 < d ≤ 3, which we determine exactly. We also discuss the quantum-to-classical crossover at small but finite temperatures, which is characterized by the appearance of multiple temperature scales. A comparison with recent results on disordered itinerant ferromagnets is given.     

Ising-type critical exponents of the fully frustrated spin-1/2 Heisenberg FM/AF square bilayer at a critical magnetic field

The fully frustrated spin-1/2 Heisenberg FM/AF square bilayer in a magnetic field with the ferromagnetic inter-dimer interaction and the antiferromagnetic intra-dimer interaction is explored by the use of localized many-magnon approach, which allows to connect the original purely quantum Heisenberg spin model on a square bilayer with the effective ferromagnetic Ising model on a simple square lattice. Magnetization and specific heat are investigated exactly at a field-driven phase transition from the singlet-dimer phase towards the fully saturated ferromagnetic phase, which changes from a discontinuous phase transition to a continuous one at a certain critical temperature. The mapping correspondence between the spin-1/2 Heisenberg FM/AF square bilayer and the ferromagnetic Ising square lattice suggests for this special critical point of the spin-1/2 Heisenberg FM/AF square bilayer critical exponents from the standard two-dimensional Ising universality class.     

Transition from orbital liquid to Jahn-Teller insulator in orthorhombic perovskites RTiO3

Following the same strategy used for RVO3, thermal conductivity measurements have been made on a series of single-crystal perovskites RTiO3 (R=La,Nd,...,Yb). Results reveal explicitly a transition from an orbital liquid to an orbitally ordered phase at a magnetic transition temperature, which is common for both the antiferromagnetic and ferromagnetic phases in the phase diagram of RTiO3. This spin/orbital transition is consistent with the mode softening at T_{N} in antiferromagnetic LaTiO3 and is supported by an anomalous critical behavior at T_{c} in ferromagnetic YTiO3.     

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.     

Variational method in hamiltonian lattice gauge theories

A general expression for the expectation value of the hamiltonian of a d + 1 dimensional lattice gauge theory as a function of the norm of the variational state (that itself has the form of a partition function of a d-dimensional lattice gauge theory) is given. Applications include U(1), SU(2), U(2) and U(N) gauge theories for large N in d = 2 + 1 dimensions. It is also demonstrated that the deconfining phase transition is of first order in every dimension above the critical one, provided it is of first or second order at the critical dimension.