This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

Physical Review B

Critical phenomena and renormalization-group theory

Within the past 20 years or so, there has occurred an explosion of interest in the magnetic behavior of pyrochlore oxides of the type $A_{2}^{3+}$$B_{2}^{4+}$O$_{7}$ where $A$ is a rare-earth ion and $B$ is usually a transition metal. Both the $A$ and $B$ sites form a network of corner-sharing tetrahedra which is the quintessential framework for a geometrically frustrated magnet. In these systems the natural tendency to form long range ordered ground states in accord with the Third Law is frustrated, resulting in some novel short range ordered alternatives such as spin glasses, spin ices and spin liquids and much new physics. This article attempts to review the myriad of properties found in pyrochlore oxides, mainly from a materials perspective, but with an appropriate theoretical context.

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Magnetic Pyrochlore Oxides

An introductory review of various concepts about first-order phase transitions is given. Rules for classification of phase transitions as second or first order are discussed, as well as exceptions to these rules. Attention is drawn to the rounding of first-order transitions due to finite-size or quenched impurities. Computational methods to calculate phase diagrams for simple model Hamiltonians are also described. Particular emphasis is laid on metastable states near first-order phase transitions, on the 'stability limits' of such states (e.g. the 'spinodal curve' of the gas-liquid transition) and on the dynamic mechanisms by which metastable states decay (nucleation and growth of droplets of a new phase, etc.).

https://iopscience.iop.org/article/10.1088/0034-4885/50/7/001/pdf

Theory of first-order phase transitions

We investigate the nature of phase transitions in a generalized uniformly frustrated square-lattice model with XY spins. The frustration is made to vary by changing the negative bond strength \ensuremath{\eta}. From ground-state (GS) analysis we find that, below the critical value \ensuremath{\eta}=(1/3), the GS is ferromagnetic, while for \ensuremath{\eta}g(1/3), it is doubly degenerate with canted spin configurations. This suggests the existence of an Ising-like transition. This is confirmed by our extensive Monte Carlo simulations. In addition, there is a Kosterlitz-Thouless-like transition at higher temperature for \ensuremath{\eta}\ensuremath{\ne}1. In the fully frustrated case (\ensuremath{\eta}=1), these two transitions are merged into a single one of dominant Ising character. These conclusions follow from a finite-size-scaling analysis and a visualization of the ordering.

Phase transitions in two-dimensional uniformly frustrated XY spin systems

The microscopic mechanism of the melting of a crystal is analyzed by the constant-pressure Monte Carlo simulation of a Lennard-Jones fcc system. Beyond a temperature of the order of 0.8 of the melting temperature, we found that the relevant excitations are lines of defects. Each of these lines has the structure of a random walk of various lengths on an fcc defect lattice. We identify these lines with the dislocation ones proposed in recent phenomenological theories of melting. Near melting we find the appearance of long lines that cross the whole system. We suggest that these long lines are the precursor of the melting process.

Dislocation Lines as the Precursor of the Melting of Crystalline Solids Observed in Monte Carlo Simulations

We study a model of phantom tethered membranes, embedded in three-dimensional space, by extensive Monte Carlo simulations. The membranes have hexagonal lattice structure where each monomer is interacting with six nearest-neighbors (NN). Tethering interaction between NN, as well as curvature penalty between NN triangles are taken into account. This model is new in the sense that NN interactions are taken into account by a truncated Lennard-Jones potential including both repulsive and attractive parts. The main result of our study is that the system undergoes a first-order crumpling transition from low-temperature flat phase to high-temperature crumpled phase, in contrast with early numerical results on models of tethered membranes.

https://arxiv.org/pdf/cond-mat/0207060.pdf

First-order transition of tethered membranes in three-dimensional space.

Etude theorique detaillee des effets quantiques sur les aimantations des surfaces dans les films minces antiferromagnetiques possedant des spins de Heisenberg (S=1/2). Le systeme etudie est un film a reseau cubique centre avec des surfaces (001). En utilisant la technique de la fonction de Green, on obtient les aimantations autocoherentes des couches a une temperature quelconque pour un ensemble donne de parametres de la surface. A hautes temperatures, l'aimantation de la couche est la plus faible a la surface et croit graduellement vers l'interieur (volume). Cependant, aux basses temperatures, on observe un comportement inhabituel des aimantations des couches au voisinage de la surface: l'aimantation de la seconde couche est inferieure a l'aimantation de la surface. Interpretation de cette anomalie comme un effet des fluctuations quantiques

Quantum effects in Heisenberg antiferromagnetic thin films

The nature of the phase transition of the nearest-neighbor Heisenberg antiferromagnet on a fcc lattice is studied by means of Monte Carlo simulations. Using a finite-size scaling, the transition is shown to be unambiguously of first order. Evidence for a first-order transition in the corresponding XY model is also presented.

Hung T. Diep

Papers

Phase transitions in two-dimensional uniformly frustrated XY spin systems

Dislocation Lines as the Precursor of the Melting of Crystalline Solids Observed in Monte Carlo Simulations

First-order transition of tethered membranes in three-dimensional space.

Quantum effects in Heisenberg antiferromagnetic thin films

First-order phase transition in the fcc Heisenberg antiferromagnet