We calculate the susceptibility amplitude ratio near a generic higher character Lifshitz point up to one-loop order. We employ a renormalization group treatment with $L$ independent scaling transformations associated to the various inequivalent subspaces in the anisotropic case in order to compute the ratio above and below the critical temperature and demonstrate its universality. Furthermore, the isotropic results with only one type of competition axes have also been shown to be universal. We describe how the simpler situations of $m$-axial Lifshitz points as well as ordinary (noncompeting) systems can be retrieved from the present framework.
The susceptibility amplitude ratio in the neighborhood of a uniaxial Lifshitz point is calculated at one-loop level using field-theoretic and $ε_{L}$-expansion methods. We use the Schwinger parametrization of the propagator in order to split the quadratic and quartic part of the momenta, as well as a new special symmetry point suitable for renormalization purposes. For a cubic lattice (d = 3), we find the result $\frac{C_{+}}{C_{-}} = 3.85$.
The thermally activated flips of the local spontaneous polarization in relaxors were simulated to investigate the effects of the applied-ac-field amplitude on the dielectric susceptibility. It was observed that the susceptibility increases with increasing the amplitude at low temperatures. At high temperatures, the susceptibility experiences a plateau and then drops. The maximum in the temperature dependence of susceptibility shifts to lower temperatures when the amplitude increases. A similarity was found between the effects of the amplitude and frequency on the susceptibility.
The high-temperature susceptibility of the $q$-state Potts model behaves as $Γ|T-T_c|^{-γ}$ as $T\to T_c+$, while for $T\to T_c-$ one may define both longitudinal and transverse susceptibilities, with the same power law but different amplitudes $Γ_L$ and $Γ_T$. We extend a previous analytic calculation of the universal ratio $Γ/Γ_L$ in two dimensions to the low-temperature ratio $Γ_T/Γ_L$, and test both predictions with Monte Carlo simulations for $q=3$ and 4. The data for $q=4$ are inconclusive owing to large corrections to scaling, while for $q=3$ they appear consistent with the prediction f…
We analyze Monte Carlo simulation and series-expansion data for the susceptibility of the three-state Potts model in the critical region. The amplitudes of the susceptibility on the high- and the low-temperature sides of the critical point as extracted from the Monte Carlo data are in good agreement with those obtained from the series expansions and their (universal) ratio compares quite well with a recent quantum field theory prediction by Delfino and Cardy.
We present a new way of probing the universality class of the site-diluted two-dimensional Ising model. We analyse Monte Carlo data for the magnetic susceptibility, introducing a new fitting procedure in the critical region applicable even for a single sample with quenched disorder. This gives us the possibility to fit simultaneously the critical exponent, the critical amplitude and the sample dependent pseudo-critical temperature. The critical amplitude ratio of the magnetic susceptibility is seen to be independent of the concentration $q$ of the empty sites for all investigated values of $q\…
We study the nature of domain walls in an ordered phase in the phase-competing region of two Ising-type order parameters. Considering a two-component $ϕ^4$ theory, we show that the domain wall of the ground-state (primary) order parameter shows a second-order phase transition associated with the secondary order parameter of the competing phase; the effective theory of the phase transition is given by the Landau theory of Ising-type phase transition. We find that the phase boundary of this phase transition is different from the spinodal line of the competing order. Experimentally, the phase tra…
The amplitude mode is a ubiquitous collective excitation in condensed matter systems with broken continuous symmetry. It is expected in antiferromagnets, short coherence length superconductors, charge density waves, and lattice Bose condensates. Its detection is a valuable test of the corresponding field theory, and its mass gap measures the proximity to a quantum critical point. However, since the amplitude mode can decay into low-energy Goldstone modes, its experimental visibility has been questioned. Here we show that the visibility depends on the symmetry of the measured susceptibility. Th…
The amplitude ratio of the susceptibility (or second size-moment) for two-dimensional percolation is calculated by two series methods and also by Monte-Carlo simulation. The first series method is a new approach based upon integrating approximations to the scaling function. The second series method directly uses low- and high-density series expansions of the susceptibility, going to unprecedented orders for both bond and site percolation on the square lattice. Putting all methods together we find a consistent value $Γ^{-}/Γ^{+} = 162.5 \pm 2$, a significant improvement over previous results th…
The dynamic magnetization-reversal phenomena in the Ising model under a finite-duration external magnetic field competing with the existing order for $T<T_c^0$ has been discussed. The nature of the phase boundary has been estimated from the mean-field equation of motion. The susceptibility and relaxation time diverge at the MF phase boundary. A Monte Carlo study also shows divergence of relaxation time around the phase boundary. Fluctuation of order parameter also diverge near the phase boundary. The behavior of the fourth order cumulant shows two distinct behavior: for low temperature and pul…
We calculate the critical amplitudes of the Polyakov loop and its susceptibility at the deconfinement transition of (3+1) dimensional SU(2) gauge theory. To this end we study the corrections due to irrelevant exponents in the scaling functions. As a guiding line for determining the critical amplitudes we use envelope equations which we derive from the finite size scaling formulae of the observables. We have produced new high precision data on N^3 x 4 lattices for N=12,18,26 and 36. With these data we find different corrections to the asymptotic scaling behaviour above and below the transition.…
We present analytical and numerical results for the specific heat and susceptibility amplitude ratios in parallel plate geometries. The results are derived using field-theoretic techniques suitable to describe the system in the bulk limit. Advantages and drawbacks of our method are discussed on the light of other approaches previously reported in the literature.
Monte Carlo (MC) and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the two-dimensional 4-state Potts model in the vicinity of the critical point are analysed. The role of logarithmic corrections is discussed and an approach is proposed in order to account numerically for these corrections in the determination of critical amplitudes. Accurate estimates of universal amplitude ratios $A_+/A_-$, $Γ_+/Γ_-$, $Γ_T/Γ_-$ and $R_C^\pm$ are given, which arouse new questions with respect to previous works.
Monte Carlo simulations and series expansion data for the energy, specific heat, magnetization and susceptibility of the 3-state Potts model on the square lattice are analyzed in the vicinity of the critical point in order to estimate universal combinations of critical amplitudes.
A discussion is presented on the crossover of the susceptibility from mean-field to Ising critical behavior upon approaching the critical point from below and from above Tc, both for He3 and Xe. Fits of the experimental susceptibility data are made to curves from Monte Carlo simulations, and the corresponding Ginzburg numbers Gi for each measured property i are deduced. Also the first correction amplitudes for the confluent singularities are obtained from the fit of the data. The respective ratios of these numbers and those obtained for the coexistence curves for He3 and Xe, presented elsewher…
Among the frustrated magnetic materials, spin-ice stands out as a particularly interesting system. Residual entropy, freezing and glassiness, Kasteleyn transitions and fractionalisation of excitations in three dimensions all stem from a simple classical Hamiltonian. But is the usual spin-ice Hamiltonian a correct description of the experimental systems? Here we address this issue by measuring magnetic susceptibility in the two most studied spin-ice compounds, Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$, using a vector magnet. Using these results, and guided by a theoretical analysis of possible di…
We compute a number of universal amplitude ratios in the three-dimensional Ising universality class. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. For example, we obtain A_+/A_-=0.536(2) and C_+/C_-=4.713(7), where A_+- and C_+- are the amplitudes of the specific heat and the magnetic susceptibility, respectively. The subscripts + and - indicate the high and the low temperature phase, respectively. We compare our results with those obtained from previous Monte Carlo simulations, high and low temperature series expansions, field t…
We study a system of particles in two dimensions interacting via a dipolar long-range potential $D/r^3$ and subject to a square-lattice substrate potential $V({\bf r})$ with amplitude $V$ and lattice constant $b$. The isotropic interaction favors a hexagonal arrangement of the particles with lattice constant $a$, which competes against the square symmetry of the substrate lattice. We determine the minimal-energy states at fixed external pressure $p$ generating the commensurate density $n = 1/b^2 = (4/3)^{1/2}/a^2$ in the absence of thermal and quantum fluctuations, using both analytical and nu…
The quench dynamics of a system involving two competing orders is investigated using a Ginzburg-Landau theory with relaxational dynamics. We consider the scenario where a pump rapidly heats the system to a high temperature, after which the system cools down to its equilibrium temperature. We study the evolution of the order parameter amplitude and fluctuations in the resulting time dependent free energy landscape. Exponentially growing thermal fluctuations dominate the dynamics. The system typically evolves into the phase associated with the faster-relaxing order parameter, even if it is not t…
Monte Carlo and series expansion data for the energy, specific heat, magnetisation and susceptibility of the 4-state Potts model in the vicinity of the critical point are analysed. The role of logarithmic corrections is discussed. Estimates of universal ratios A_+/A_-, $Γ_+/Γ_L$, $Γ_T/Γ_L$ and R_c^+ are given.
We study the phase behaviour of a fluid composed of particles which interact via a pair potential that is repulsive for large inter-particle distances, is attractive at intermediate distances and is strongly repulsive at short distances (the particles have a hard core). As well as exhibiting gas-liquid phase separation, this system also exhibits phase transitions from the uniform fluid phases to modulated inhomogeneous fluid phases. Starting from a microscopic density functional theory, we develop an order parameter theory for the phase transition in order to examine in detail the phase behavi…
