Search results for "statistical physics"
showing 10 items of 1402 documents
Computer simulations of a Lennard-Jones model for Ar1—x(N2)x: A prototype system for quadrupolar glasses
1998
Abstract Recent theoretical studies of orientational ordering in pure and diluted nitrogen crystals are summarized. While pure N2 has a first order phase transition from a plastic crystal to a phase with long-range orientational order, dilution with argon atoms leads to a quadrupolar glass phase. Monte Carlo simulations are used to study these phases, considering also the behavior of isolated N2 impurities in Ar crystals. It is shown that a simple model that neglects electrostatic interactions and takes only Lennard-Jones interactions into account can describe already many properties in qualitative agreement with experiment. Even the slow dynamics of the quadrupole moments can be modeled by…
Simplified Monte Carlo simulations of point defects during industrial silicon crystal growth
2004
Abstract The paper proposes Monte-Carlo method-based 2D and 3D models of vacancies and interstitials in a cubic crystal. The model exploits the concept of lattice gas with covalent bounds between neighbour nodes. Two lattices shifted by half-period serve as nodes for atoms of the main crystal and interstitials. Distribution of particles between both lattices characterizes the entropy of the crystal. Successfully chosen interaction energies between main and sub-lattices allows the authors to detect a phase transition solid–liquid as well as to study the production of crystal defects/their agglomeration as a function of cooling/heating rate. Although the introduced 3D modification of the mode…
MONTE CARLO METHODS FOR FIRST ORDER PHASE TRANSITIONS: SOME RECENT PROGRESS
1992
This brief review discusses methods to locate and characterize first order phase transitions, paying particular attention to finite size effects. In the first part, the order parameter probability distribution and its fourth-order cumulant is discussed for thermally driven first-order transitions (the 3-state Potts model in d=3 dimensions is treated as an example). First-order transitions are characterized by a minimum of the cumulant, which gets very deep for large enough systems. In the second part, we discuss how to locate first order phase boundaries ending in a critical point in a large parameter space. As an example, the study of the unmixing transition of asymmetric polymer mixtures…
Quantum Critical Scaling under Periodic Driving
2016
Universality is key to the theory of phase transition stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model's microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time $\tau_{bd}$, proportional to the size of the system. This behavio…
Energy fluctuations and the singularity of specific heat in a 3D Ising model
2004
We study the energy fluctuations in 3D Ising model near the phase transition point. Specific heat is a relevant quantity which is directly related to the mean squared amplitude of the energy fluctuations in the system. We have made extensive Monte Carlo simulations in 3D Ising model to clarify the character of the singularity of the specific heat C v based on the finite-size scaling of its maximal values C v max depending on the linear size of the lattice L . An original iterative method has been used which automatically finds the pseudocritical temperature corresponding to the maximum of C v . The simulations made up to L ≤ 128 with application of the Wolff's cluster algorithm allowed us t…
Classification theory for anequilibrium phase transitions
1993
The paper introduces a classification of phase transitions in which each transition is characterized through its generalized order and a slowly varying function. This characterization is shown to be applicable in statistical mechanics as well as in thermodynamics albeit for different mathematical reasons. By introducing the block ensemble limit the statistical classification is based on the theory of stable laws from probability theory. The block ensemble limit combines scaling limit and thermodynamic limit. The thermodynamic classification on the other hand is based on generalizing Ehrenfest's traditional classification scheme. Both schemes imply the validity of scaling at phase transition…
Critical Phenomena at the Surface of Systems Undergoing a Bulk First Order Transition: Are They Understood?
2002
Systems that exhibit a first-order phase transition in the bulk, such as binary alloys where the order parameter vanishes discontinuously at some critical value of a control parameter, may show a continuous vanishing of the local order parameter at the surface. This “surface-induced disordering” is described theoretically as a variant of critical wetting, where an interface between the locally disordered surface and the ordered bulk gradually moves towards the bulk. We test this description by Monte Carlo simulations for a body centered cubic model alloy, with interactions between nearest and next nearest neighbors, for which the phase diagram in the bulk has been calculated very accurately…
Theory of Nuclear Quantum Dynamics Simulations
2016
In Chap. 2, we have seen that the theoretical study of a molecular system is, in a vast majority of cases, separated in two steps. In a first step, the electronic structure of the system is studied by solving the electronic Schrodinger equation with fixed nuclei. This approach, combined with geometry optimization techniques, allows one to locate the important features of the various potential energy surfaces (PESs) of the electronic states of interest. In the context of photochemistry, as seen in Chap. 3, this approach allows one to characterize the various decay pathways of the molecule after photoexcitation. This information can then be used to interpret the various decay time constants o…
Roadmap on STIRAP applications
2019
STIRAP (stimulated Raman adiabatic passage) is a powerful laser-based method, usually involving two photons, for efficient and selective transfer of populations between quantum states. A particularly interesting feature is the fact that the coupling between the initial and the final quantum states is via an intermediate state, even though the lifetime of the latter can be much shorter than the interaction time with the laser radiation. Nevertheless, spontaneous emission from the intermediate state is prevented by quantum interference. Maintaining the coherence between the initial and final state throughout the transfer process is crucial. STIRAP was initially developed with applications in …
Bounds on mixed state entanglement
2020
In the general framework of d 1 ×