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Magnetic monopoles have eluded experimental detection since their prediction nearly a century ago by Dirac. Recently it has been shown that classical analogues of these enigmatic particles occur as excitations out of the topological ground state of a model magnetic system, dipolar spin ice. These quasi-particle excitations do not require a modification of Maxwell's equations, but they do interact via Coulombs law and are of magnetic origin. In this paper we present an experimentally measurable signature of monopole dynamics and show that magnetic relaxation measurements in the spin ice material $Dy_{2}Ti_{2}O_{7}$ can be interpreted entirely in terms of the diffusive motion of monopoles in the grand canonical ensemble, constrained by a network of "Dirac strings" filling the quasi-particle vacuum. In a magnetic field the topology of the network prevents charge flow in the steady state, but there is a monopole density gradient near the surface of an open system

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The probability density function (PDF) of a global measure in a large class of highly correlated systems has been suggested to be of the same functional form. Here, we identify the analytical form of the PDF of one such measure, the order parameter in the low temperature phase of the 2D-XY model. We demonstrate that this function describes the fluctuations of global quantities in other correlated, equilibrium and non-equilibrium systems. These include a coupled rotor model, Ising and percolation models, models of forest fires, sand-piles, avalanches and granular media in a self organized critical state. We discuss the relationship with both Gaussian and extremal statistics.PACS numbers: 05.40, 05.65, 47.27, 68.35.Rh Self similarity is an important feature of the natural world. It arises in strongly correlated many body systems when fluctuations over all scales from a microscopic length a to a diverging correlation length ξ lead to the appearence of "anomalous dimension" [1] and fractal properties. However, even in an ideal world the divergence of of ξ must ultimately be cut off by a macroscopic length L, allowing the definition of a range of scales between a and L, over which the anomalous behaviour can occur. Such systems are found, for example, in critical phenomena, in Self-Organized Criticality [2,3] or in turbulent flow problems. By analogy with fluid mechanics we shall call these finite size critical systems "inertial systems" and the range of scales between a and L the "inertial range". One of the anomalous statistical properties of inertial systems is that, whatever their size, they can never be divided into mesoscopic regions that are statistically independent. As a result they do not satisfy the basic criterion of the central limit theorem and one should not necessarily expect global, or spatially averaged quantities to have Gaussian fluctuations about the mean value. In Ref.[4](BHP) it was demonstrated that two of these systems, a model of finite size critical behaviour and a steady state in a closed turbulent flow experiment, share the same non-Gaussian probability distribution function (PDF) for fluctuations of global quantities. Consequently it was proposed that these two systems -so utterly dissimilar in regards to their microscopic details -share the same statistics simply because they are critical. If this is the case, one should then be able to describe turbulence as a finite-size critical phenomenon, with an effective "universality class". As, however, turbulence and the magnetic model are very unlikely to share the same universality class, it was implied that the differences that separate critical phenomena into universality classes represent at most a minor perturbation on the functional form of the PDF. In this paper, to test this proposition, we determine the functional form of the BHP fluctuation spectrum and show that it indeed applies to a large class of inertial systems [5].The magnetic model studied by BHP, the spin wave limit to the two dimensional XY (2D-XY) model, is defined by ...

The Coulomb phase, with its dipolar correlations and pinch-point-scattering patterns, is central to discussions of geometrically frustrated systems, from water ice to binary and mixed-valence alloys, as well as numerous examples of frustrated magnets. The emergent Coulomb phase of lattice-based systems has been associated with divergence-free fields and the absence of long-range order. Here, we go beyond this paradigm, demonstrating that a Coulomb phase can emerge naturally as a persistent fluctuating background in an otherwise ordered system. To explain this behavior, we introduce the concept of the fragmentation of the field of magnetic moments into two parts, one giving rise to a magnetic monopole crystal, the other a magnetic fluid with all the characteristics of an emergent Coulomb phase. Our theory is backed up by numerical simulations, and we discuss its importance with regard to the interpretation of a number of experimental results

We examine the statistical mechanics of spin-ice materials with a [100] magnetic field. We show that the approach to saturated magnetization is, in the low-temperature limit, an example of a 3D Kasteleyn transition, which is topological in the sense that magnetization is changed only by excitations that span the entire system. We study the transition analytically and using a Monte Carlo cluster algorithm, and compare our results with recent data from experiments on Dy2Ti2O7.

We study the probability density function for the fluctuations of the magnetic order parameter in the low-temperature phase of the XY model of finite size. In two dimensions, this system is critical over the whole of the low-temperature phase. It is shown analytically and without recourse to the scaling hypothesis that, in this case, the distribution is non-Gaussian and of universal form, independent of both system size and critical exponent eta. An exact expression for the generating function of the distribution is obtained, which is transformed and compared with numerical data from high-resolution molecular dynamics and Monte Carlo simulations. The asymptotes of the distribution are calculated and found to be of exponential and double exponential form. The calculated distribution is fitted to three standard functions: a generalization of Gumbel's first asymptote distribution from the theory of extremal statistics, a generalized log-normal distribution, and a chi(2) distribution. The calculation is extended to general dimension and an exponential tail is found in all dimensions less than 4, despite the fact that critical fluctuations are limited to D=2. These results are discussed in the light of similar behavior observed in models of interface growth and for dissipative systems driven into a nonequilibrium steady state.

AbstracL Layered magneu, considered to be experimental realizations of the w XY model, have a magnetization with a characteristic exponent @ = 0 . 2 . We show, using modified renormalization group equations, that this value of fl is a universal signature of finite-sized w XY behaviour. We present simulation data in agreement with both the calculation and the experimental observations.The two-dimensional XY model has long presented an interesting problem to both theoreticians [I] and experimentalists [2-S]. In the thermodynamic limit, at finite temperatures and in zero magnetic field the model cannot sustain long-range order 191, but nevertheless exhibits a Xosterlitz-Thouless-Berezinsldi' phase transition [lo] involving the unbinding of spin vortices at a critical temperature TKT. In the lowtemperature phase of bound vortices the correlation length remains infinite and the magnetization zero, as a result of the excitation of long-wavelength spin waves. The critical exponents q and 6 vary continuously with temperature [ll], but the exponents p, 7 and U are undefined.Layered Heisenberg magnets with planar anisotropy can be treated as quasi-zD XY systems [12]. In these materials the spontaneous magnetization is stabilized by weak 3D coupling J' which determines the asymptotic critical behaviour. However at lower temperature there is a very sharp crossover to a second regime, which we refer to as 'sub-critical'. The magnetization exponents p measured in thi range are listed in table 1. The compounds BaNi,(PO,),, Rb,CrCI, and K,CuF, are the best approximations to the ideal and represent a variety of lattice types, spin values and degrees of planar anisotropy. All have a well defined p = 0.23. The other compounds in the list have p varying between Using modified renormalization group (RG) equations, we show that the magnetization of an arbitrarily large, but finite, ZD XY model approaches power-law behaviour over a restricted temperature range, with an effective exponent p = 0.23.Thii is a universal properly of the ZDXYmodel and can be regarded, when observed in experiment, as a signature of ZD XY behaviour. We present Monte Carlo simulations in agreement with our calculation, and finally discuss the relationship between the calculation, and the experimental results of table 1.Although there is no broken symmetry in the ZD XY model [9] the spin-spin correlation function has power-law decay at low temperature. This slow decay with 0.18 and -z 0.26 [13].