Session Q19: Ising, Spin Glass, Frustrated Magnets

Thermodynamics of the two-dimensional random-bond Ising model

The two-dimensional Ising spin glass possesses the disorder and frustration necessary to describe the rich behavior found in glassy materials with complex free-energy landscapes. Recently-developed exact algorithms for this model with arbitrary quenched bond disorder have allowed for equilibrium simulations of systems far larger than those accessible by other methods. We use a Pfaffian technique to measure thermodynamic quantities such as the specific heat and the domain-wall free energy to characterize the phase transitions in this model as either temperature or disorder strength is varied. We also present precision measurements on the disorder-temperature phase diagram of this model, including a detailed study of the reentrance that has been seen for bimodal disorder.   

Competing Low-Temperature Phases in a Dilute Ising Magnet

LiHo(x)Y(1-x)F4 serves as a physical manifestation of the Ising model in transverse field with controllable disorder. At dilute Ho3+ dipole concentration, the combination of ferromagnetic and antiferromagnetic couplings via the spatial anisotropy of the dipolar coupling, disorder, and random internal fields combine to produce a variety of possible ground states. We show for x = 0.045 the ability to choose between spin liquid and spin glass behavior with proper thermal preparation. We present both linear and nonlinear magnetic susceptibility data as well as magnetic pump/probe techniques to quantify the stability of the liquid, and to probe the coupling between the spin states and the nuclear spin bath.   

The $p,q$-binomial distribution applied to the Ising model

Monte Carlo simulations have shown that the $p,q$-binomial distribution closely fits the magnetisation distribution for the $d$-dimensional Ising model at all temperatures when $d>4$. It also fits well for some temperatures near $T_c$ for $d=2,3$ and especially so for $d=4$. At high and low temperatures, away from $T_c$, the $p,q$-distribution always fits extremely well. However, it appears very difficult to determine how the parameters $p$ and $q$ depend of the temperature. From high and low temperature series expansions we can get partial results on their temperature dependence. Near $T_c$ for $d=5$ we have approximately that $p=1-0.0736/L^5$ and $q=1-9.87/L^5$ whereas for $d<5$ the linear coefficient of $q$ grows logarithmically. We show numerically how the parameters behave near $T_c$ with increasing $d$.   

An ab initio study of radiation damage effects on the magnetic structure of bulk Iron

A fundamental understanding of radiation damage effects in solids is of great importance in assisting the development of structural materials with improved mechanical properties for nuclear energy applications. In this presentation, we discuss our recent theoretical investigation on the magnetic structure evolution in bulk Fe after an energetic particle has disturbed the lattice by a displacement cascade. We applied a linear scaling ab initio method to the study of magnetic moment distributions in a low energy cascade for a series of time steps. The primary damage state and the evolution of the defects were simulated using molecular dynamics with a Finnis-Sinclair interatomic potential. We will show the statistics of the magnetic moments in the sample and discuss its relationship with the atomic volume distribution.   

Chaos, broken hyperscaling, and nonuniversality in a spin glass

Recently extended precise numerical methods and newly modified scaling arguments allow for a coherent picture of the glassy state in a two-dimensional spin glass to be assembled. This glassy state, where the correlation length is larger than the system size, is characterized by ``chaos,'' the extreme sensitivity of the state to temperature. This chaos is shown to lead to a breakdown of hyperscaling in spin glasses. The length scale at which entropy becomes important is found to depend on the type of randomness, so that though there is a type of universality, the critical exponents depend on the distribution of disorder. The numerical simulations use multiprecision arithmetic to exactly compute the partition function in samples of sizes up to $L^2=512^2$ down to temperatures of less than $J/20$, where the typical strength of the disorder is $J$. These results can be used in support of studies of the non-equilibrium behavior of glassy models.   

Disordered Pinned Anyons in Two Dimensions

We consider the effect of disorder on the behavior of pinned anyons in two spatial dimensions. Within an approximate numerical strong disorder renormalization group (SDRG) treatment, we find that both Fibonacci and Majorana anyons exhibit flows back to weaker disorder rather than toward infinite randomness phases such as those they exhibit in d=1. Restricting to the technically simpler Majorana anyons, we map out the effects of sign and coupling strength disorder on the proposed translation invariant topological liquid found in the absence of disorder. In disordered Hall bars, the nature of this descendant phase, and in particular its localization properties, may be relevant to the interpretation of transport and non-Abelian interferometry.   

Effective potential study of the Diluted Antiferromagnet in a Field

We present a numerical study of the three-dimensional Diluted Antiferromagnet in a Field (DAFF), one of the experimental realizations of the Random Field Ising Model. We work in a constrained ensemble (tethered ensemble) where the Helmholtz effective potential is featured, rather than the free energy. Our method cures the problem of a strong violation of self-averaging, thus allowing us to compute the correlation length for systems sizes up to $L=32$. This quantity, when measured in units of the lattice size, is independent of the system size at the critical point, a strong indication of a second-order phase transition. This scale invariance allows us to apply finite-size scaling in the form of Nightingale's phenomenological renormalization. We obtain accurate estimates of the critical exponents. Since our method reconstructs the effective potential, we can also compute accurately the hyperscaling violation exponent. We perform as well an investigation of the geometrical properties of the instanton-like configurations, namely, the minimal cost configurations joining the two ordered phases. This study sheds light on previous claims of a first-order phase transition in this system.   

Quantum Fidelity Susceptibilities of the Anisotropic Triangular Antiferromagnet: Conjugate Field Fidelity Susceptibilities

The Heisenberg model of the Anisotropic Triangular Antiferromagnet(HATM) has seen a surge of interest owing to its relation to Cesium Copper Chloride, an inorganic salt with a potential spin-liquid phase. In this talk a new approach to quantum fidelity susceptibilities will be introduced and used to explore the phase diagram of the HATM. These fidelity susceptibilities are computable via exact diagonalization techniques and can be coupled to specific order parameters. We present results from such calculations shedding new light on the phase diagram of the Anisotropic Triangular Antiferromagnet.   

Stabilization of surface spin glass behavior in core/shell-Fe67Co33/CoFe2O4 nanoparticles

Magnetic properties of Co33Fe67--CoFe2O4 (core-shell) nanoparticles are presented. Both dc magnetization and ac susceptibility measurements indicate a spin glass (SG) like transition occurring at $T$F $\sim $175 K. The SG nature of the transition is also confirmed by the field dependence of the freezing temperature $T$F(H) following the well known Almeida--Thouless line, $\delta T$F$\sim $H$^{2/3}$. Additionally, the particles exhibit a large exchange bias ($H$EB $\sim $ 1357 Oe) arising from the core-shell (ferromagnetic-SG) coupling. The unusually high SG transition temperature and large exchange bias effects are attributed to a combination of several factors including the thickness of the amorphous oxide shell and large values of the exchange and anisotropy constants associated with the CoFe2O4 shell.   

Critical Behavior of L\'evy Spin Glasses

Universality, one of the foundations of the theory of critical phenomena, is well established for many problems in statistical physics. However, there is still debate if changing the disorder between the spins-spin interactions in spin glasses can influence the universality class of the system. This apparent violation of universal behavior can be attributed to the numerical complexity of these systems which limits simulations to small systems sizes, typically paired with strong corrections to scaling. Although it is well established that universality is not violated for nearest-neighbor spin glasses with compact disorder distributions (e.g., Gaussian and bimodal), some studies suggest that this might not be the case when the disorder distributions are broad, as in the case of the L\'evy distribution. Using large-scale Monte Carlo simulations that combine parallel tempering with specialized cluster moves, as well as innovative scaling techniques, we show that L\'evy spin glasses do obey universality for the system sizes studied. Furthermore, we probe recent analytical predictions made for the critical temperature of L\'evy spin glasses as a function of the disorder distribution width.   

Spin glasses on scale-free networks: Simple models to describe opinion formation?

We study the critical behavior of Ising spin glasses on scale-free networks using large-scale Monte Carlo simulations. Our results show that when the exponent that describes the decay of the interaction degree in the scale-free graph is strictly larger than 3 the system undergoes a finite-temperature spin-glass transition. However, when the exponent is equal to or less than 3, the spin-glass phase is stable for all temperatures. This robustness to local (temperature) perturbations and global biases (field) is compared to experimental data from social networks.   

Using Azimuthal Hysteresis for Determining the Anti-ferromagnet Moment Density at the Spin Glass Interface: The case of BFO

We report a systematic procedure for extracting the anisotropies, exchange energies and the surface anti-ferromagnet (AFM) moment of AFM-ferromagnet (FM) systems that show spin glass (SG) behavior. In any SG system, the hysteresis characteristics at a critical angle combined with the azimuthal hysteresis properties give important information about the surface AFM moment density and the coupling energy. Using this scheme we report the interface magnetic energy parameters of the epitaxial BFO-FM system. We find a single value for the interface coupling energy that reproduces both the exchange bias and the enhancement. Our extracted surface AFM moment density is of the order of the FM moment density that is independent of the FM material used. The high moment density on the BFO surface indicates a significant magnetic property modification at the BFO-FM interface. The implication of the presence of this high AFM moment is discussed in the context of achieving deterministic electric field driven magnetic moment switching.   

Study of the Gr\"{u}neisen Parameters at a Field-induced Quantum Critical Point in NiCl2-SC(NH2)2

NiCl$_{2}$-SC(NH$_{2})_{2}$, also known as DTN, is a quantum paramagnet, where the Ni$^{2+}$ single ion anisotropy $D$ = 8.9K opens an energy gap between the $S_{z}$ = 0 ground state and the $S_{z}=\pm $1 exited state. In this material an XY-antiferromagnetic ordered state is induced at low temperatures by applying magnetic fields between $H_{c1} \quad \approx $ 2T and $H_{c2}$ = 10.5T. At the phase boundaries critical exponents consistent with Bose-Einstein condensation of magnons are found. Here we present investigations of quantum criticality close to $H_{c1}$ by thermal expansion, magnetization and specific heat measurements. Our data reveal a divergency for T$\to $ 0 of the thermal and magnetic Gr\"{u}neisen parameters as expected for a quantum critical point of a diluted Bose gas.   

Characteristic time scales and overlap distributions in replica exchange Monte Carlo simulations of spin glasses

We present a large-scale numerical study using replica exchange Monte Carlo (parallel tempering) of time scales of the three- dimensional Ising spin glass. We measure the integrated and exponential autocorrelation times for several observables, as well as the round-trip times for different disorder realizations in order to investigate the relationship between the characteristic time scales of a disorder realization and its overlap distribution.