Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.     

The role of dipolar interaction in nanocomposite permanent magnets

The effects of dipolar interactions on the magnetization behaviors and magnetic properties of the nanocomposite magnets have been studied by micromagnetic simulations. Numerical results show that the dipolar interaction plays an important role during the demagnetization process, especially in the magnets with large soft-phase content _vs$v_{\mathrm{s}}$. For the isotropic nanocomposites, the remanence enhancement can be controlled through adjustments of the grain size D   and _vs$v_{\mathrm{s}}$. However, the appearance of magnetic vortex state leads to a very low remanence in the magnets with large D   and _vs$v_{\mathrm{s}}$. The dependence of coercivity on D   and _vs$v_{\mathrm{s}}$ can be attributed to the exchange-induced magnetization reversal near the grain boundaries and the low nucleation field of soft phase, respectively. For the anisotropic nanocomposites, the reduced remanence _mr$m_{\mathrm{r}}$ is equal to 1.0$1.0$ for the magnets with small D   or with low _vs$v_{\mathrm{s}}$. However, _mr$m_{\mathrm{r}}$ decreases with increasing _vs$v_{\mathrm{s}}$ for the magnet with large D   due to the influence of dipolar interactions. The difference between the calculated coercivity _Hc$H_{\mathrm{c}}$ with and without considering dipolar interaction shows that the dipolar interaction plays a more important role during the magnetization reversal in the soft phase than that in the hard phase. The maximum calculated energy product of the isotropic nanocomposites is only about 40 MGOe due to the conflicting relation between remanence and coercivity, while that of the anisotropic nanocomposites is 112 MGOe. This reminds us that the alignment of hard grain is important to obtain high performance.     

Fluxmetric and magnetometric demagnetizing factors for cylinders

Fluxmetric and magnetometric demagnetizing factors, _Nf$N_{\mathrm{f}}$ and _Nm$N_{\mathrm{m}}$, for cylinders along the axial direction are numerically calculated as functions of material susceptibility χ$\chi$ and the ratio γ$\gamma$ of length to diameter. The results have an accuracy better than 0.1% with respect to min(_Nf,m,1-_Nf,m)$\min (N_{\mathrm{f},\mathrm{m}},1-N_{\mathrm{f},\mathrm{m}})$ and are tabulated in the range of 0.01?γ?500$0.01?\gamma ?500$ and -1?χ<∞$-1?\chi <\infty$. _Nm$N_{\mathrm{m}}$ along the radial direction is evaluated with a lower accuracy from _Nm$N_{\mathrm{m}}$ along the axis and tabulated in the range of 0.01?γ?1$0.01?\gamma ?1$ and -1?χ<∞$-1?\chi <\infty$. Some previous results are discussed and several applications are explained based on the new results.     

Comparative study between a two-dimensional anisotropic Heisenberg antiferromagnet with easy-axis single-ion anisotropy and one with easy-axis exchange anisotropy

Generally, in literature, easy-axis single ion anisotropy and easy-axis exchange anisotropy was treated in indistinct way. In this work we propose to perform a comparative study of the effects of these two easy-axis anisotropies on the behavior of the magnetization and the critical temperature (_Tc)$(T_{\mathrm{c}})$ in the 2D classical Heisenberg antiferromagnetic model. In order to study the low-temperature thermodynamics of this model, we should consider the contribution of anisotropic spin waves, using a self-consistent harmonic approximation (SCHA) theory. We compare the predictions of SCHA with numerical simulations on L×L$L\times L$ square lattices using Monte Carlo (MC) simulations, which include effects due to all thermodynamically allowed excitations. Our SCHA results are in good agreement with our MC simulations results and have shown that the strong K$K$ limit gives two different Ising-like behavior. In the exchange anisotropic case, the dependence of _Tc$T_{\mathrm{c}}$ on anisotropic parameter K$K$ becomes linear and in the single-ion anisotropic case, _Tc$T_{\mathrm{c}}$ becomes independent of K$K$. Also, using MC simulations and finite size scaling, we show that the critical exponents in the two anisotropic case are compatible with the 2D Ising values α=0.125$\alpha =0.125$ and γ=1.75$\gamma =1.75$.     

On the Riemannian geometry of Seiberg–Witten moduli spaces

We construct a natural L²$L^2$-metric on the perturbed Seiberg–Witten moduli spaces _Mμ+${\mathfrak{M}}_{{\mu }^{+}}$ of a compact 4-manifold M$M$, and we study the resulting Riemannian geometry of _Mμ+${\mathfrak{M}}_{{\mu }^{+}}$. We derive a formula which expresses the sectional curvature of _Mμ+${\mathfrak{M}}_{{\mu }^{+}}$ in terms of the Green operators of the deformation complex of the Seiberg–Witten equations. In case M$M$ is simply connected, we construct a Riemannian metric on the Seiberg–Witten principal U(1)$U\left(1\right)$ bundle P→_Mμ+$\mathfrak{P}\to {\mathfrak{M}}_{{\mu }^{+}}$ such that the bundle projection becomes a Riemannian submersion. On a Kähler surface M$M$, the L²$L^2$-metric on _Mμ+${\mathfrak{M}}_{{\mu }^{+}}$ coincides with the natural Kähler metric on moduli spaces of vortices.     

Surface magnetic phase transitions in films

Using a simple Landau model, we discuss the different possibilities of generating magnetic effects at a second-order transition for films. Varying the sample size d$d$ and/or surface coupling γ$\gamma$ one can decrease or increase substantially the surface critical temperature _Ts$T_{\mathrm{s}}$ and the saturation magnetization _Ms$M_{\mathrm{s}}$. In the case of γ>0$\gamma >0$, _Ms$M_{\mathrm{s}}$ and _Ts$T_{\mathrm{s}}$ decrease from the bulk values as the film thickness is reduced. These theoretical results are in nice agreement with the experimental data on superconducting _MgB2${\mathrm{MgB}}_2$ thin films. By contrast, for γ<0$\gamma <0$, an enhancement of both quantities is expected. This extraordinary transition has rarely been observed experimentally and, usually, the situation is far from being clear. We analyze a new experiment on _NiFe2O4${\mathrm{NiFe}}_2{\mathrm{O}}_4$ ultra-thin films, where a very strong enhancement of the saturation magnetization is observed.     

Effective cosmological constant within the expanding axion universe

We show that the value of an effective cosmological constant, _Λeff${\Lambda }_{\mathit{eff}}$, is influenced by the dimensionality of the space. Results were obtained in the framework of the axion model describing expansion of the inhomogeneous universe. _Λeff${\Lambda }_{\mathit{eff}}$ determines the tension of the space (i.e. elasticity), and is relaxed when extra dimensions are accessible. We demonstrate that the effective value of the cosmological constant may be tuned to be consistent with experimental observation. Inhomogeneities considered are representative of temperature fluctuations observed within the cosmic microwave background radiation.     

Monte Carlo calculations of the magnetocaloric effect in gadolinium

In this work we discuss the magnetocaloric effect in metallic gadolinium. We use a model Hamiltonian of interacting 4f spins and treat the 4f spin–spin interaction both in the mean field approximation and in the Monte Carlo simulation. The calculations show that the mean field approximation yields reasonable results for the magnetocaloric potentials ΔS$\mathrm{\Delta }S$ and Δ_Tad$\mathrm{\Delta }{T}_{\mathrm{ad}}$ but it fails in explaining the experimental data of specific heat at the magnetic ordering temperature. On the other hand, our theoretical results show that the Monte Carlo calculation describes well not only the magnetocaloric potentials ΔS$\mathrm{\Delta }S$ and Δ_Tad$\mathrm{\Delta }{T}_{\mathrm{ad}}$ but also the specific heat capacity.     

What if supersymmetry breaking appears below the GUT scale?

We consider the possibility that the soft supersymmetry-breaking parameters m_1/2$m_{1/2}$ and m₀$m_0$ of the MSSM are universal at some scale Min$M_{\mathrm{in}}$ below the supersymmetric grand unification scale MGUT$M_{\mathrm{GUT}}$, as might occur in scenarios where either the primordial supersymmetry-breaking mechanism or its communication to the observable sector involve a dynamical scale below MGUT$M_{\mathrm{GUT}}$. We analyze the (m_1/2,m₀)$(m_{1/2},m_0)$ planes of such sub-GUT CMSSM models, noting the dependences of phenomenological, experimental and cosmological constraints on Min$M_{\mathrm{in}}$. In particular, we find that the coannihilation, focus-point and rapid-annihilation funnel regions of the GUT-scale CMSSM approach and merge when Min∼¹⁰¹² GeV$M_{\mathrm{in}}\sim {10}^{12}\text{GeV}$. We discuss sparticle spectra and the possible sensitivity of LHC measurements to the value of Min$M_{\mathrm{in}}$.     

Transitions to chaos in the wake of an axisymmetric bluff body

This Letter aims at understanding the dynamical process that leads to the onset of chaos in the flow past a blunt-based axisymmetric bluff body. On the basis of direct numerical simulations, conducted for Reynolds numbers ranging from 100 to 900, we show that the flow undergoes multiple transitions, successively giving rise to the SS, _RSPa${\mathrm{RSP}}_a$, _RSPb${\mathrm{RSP}}_b$, _RSPc${\mathrm{RSP}}_c$ and RSB wake states. In particular, the _RSPc${\mathrm{RSP}}_c$ state, revealed in this work via long-term computations, is characterized by intermittent vortex stretching denoting the onset of chaos before the symmetry breaking and the occurrence of the RSB state.     

On leafwise conformal diffeomorphisms

For every diffeomorphism φ:M→N$\phi :M\to N$ between 3-dimensional Riemannian manifolds M$M$ and N$N$, there are locally two 2-dimensional distributions _D±$D_{\pm }$ such that φ$\phi$ is conformal on both of them. We state necessary and sufficient conditions for a distribution to be one of _D±$D_{\pm }$. These are algebraic conditions expressed in terms of the self-adjoint and positive definite operator induced from _φ∗${\phi }_{\ast }$. We investigate the integrability condition of _D+$D_{+}$ and _D−$D_{-}$. We also show that it is possible to choose coordinate systems in which leafwise conformal diffeomorphism is holomorphic on leaves.