Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states

When the two-dimensional random-bond Ising model is represented as a noninteracting fermion problem, it has the same symmetries as an ensemble of random matrices known as class D. A nonlinear sigma model analysis of the latter in two dimensions has previously led to the prediction of a metallic phase, in which the fermion eigenstates at zero energy are extended. In this paper we argue that such behavior cannot occur in the random-bond Ising model, by showing that the Ising spin correlations in the metallic phase violate the bound on such correlations that results from the reality of the Ising couplings. Some types of disorder in spinless or spin-polarized p-wave superconductors and paired fractional quantum Hall states allow a mapping onto an Ising model with real but correlated bonds, and hence a metallic phase is not possible there either. It is further argued that vortex disorder, which is generic in the fractional quantum Hall applications, destroys the ordered or weak-pairing phase, in which nonabelian statistics is obtained in the pure case.Comment: 13 pages; largely independent of cond-mat/0007254; V. 2: as publishe

Quantized Skyrmion Fields in 2+1 Dimensions

A fully quantized field theory is developped for the skyrmion topological excitations of the O(3) symmetric CP$^1$-Nonlinear Sigma Model in 2+1D. The method allows for the obtainment of arbitrary correlation functions of quantum skyrmion fields. The two-point function is evaluated in three different situations: a) the pure theory; b) the case when it is coupled to fermions which are otherwise non-interacting and c) the case when an electromagnetic interaction among the fermions is introduced. The quantum skyrmion mass is explicitly obtained in each case from the large distance behavior of the two-point function and the skyrmion statistics is inferred from an analysis of the phase of this function. The ratio between the quantum and classical skyrmion masses is obtained, confirming the tendency, observed in semiclassical calculations, that quantum effects will decrease the skyrmion mass. A brief discussion of asymptotic skyrmion states, based on the short distance behavior of the two-point function, is also presented.Comment: Accepted for Physical Review

Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

We present exact results on the partition function of the $q$-state Potts model on various families of graphs $G$ in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \{1,...,s\}$ of the total set of possible spin values, $Z(G,q,s,v,w)$, where $v$ and $w$ are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial $Ph(G,q,s,w)$ that counts the number of colorings of the vertices of $G$ subject to the condition that colors of adjacent vertices are different, with a weighting $w$ that favors or disfavors colors in the interval $I_s$. We derive powerful new upper and lower bounds on $Z(G,q,s,v,w)$ for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for $Z(G,q,s,v,w)$ on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.Comment: 39 pages, 1 figur

Possible Z2 phase and spin-charge separation in electron doped cuprate superconductors

The SU(2) slave-boson mean-field theory for the tt'J model is analyzed. The role of next-nearest-neighbor hopping t' on the phase-diagram is studied. We find a pseudogap phase in hole-doped materials (where t'<0). The pseudo-gap phase is a U(1) spin liquid (the staggered-flux phase) with a U(1) gauge interaction and no fractionalization. This agrees with experiments on hole doped samples. The same calculation also indicates that a positive t' favors a Z2 state with true spin-charge separation. The Z2 state that exists when t' > 0.5J can be a candidate for the pseudo-gap phase of electron-doped cuprates (if such a phase exists). The experimental situation in electron-doped materials is also addressed.Comment: 6 pages, 2 figures, RevTeX4. Homepage http://dao.mit.edu/~wen

The changing of the guard: groupwork with people who have intellectual disabilities

This paper considers the impact of service systems on group activities. It describes an inter-professional groupwork project facilitated by a social worker and a community nurse. The project provided an emancipatory experience for a group of adults who had intellectual disabilities. The group was charged with the task of reviewing and updating the recruitment and interview processes used by a 'Learning Disability Partnership Board', when employing new support workers. The paper begins with a brief history of intellectual disability and provides a context to the underpinning philosophical belief that people should be encouraged and supported to inhabit valued social roles no matter what disability they may have. It then identifies the ways in which the sponsoring health, education and social care services impacted on the creation and development of a groupwork project. It might have been expected that the nature of the intellectual disability would have been the major influence on group process. However the paper reveals that organisational constraints had a significant impact on group functioning. Issues including, staffing budgets and transport contracts impacted on group process and function. The results of the project show how, with adequate support, people with intellectual disability can make important decisions that have long-reaching impacts on the services

Fluctuations and Dissipation of Coherent Magnetization

A quantum mechanical model is used to derive a generalized Landau-Lifshitz equation for a magnetic moment, including fluctuations and dissipation. The model reproduces the Gilbert-Brown form of the equation in the classical limit. The magnetic moment is linearly coupled to a reservoir of bosonic degrees of freedom. Use of generalized coherent states makes the semiclassical limit more transparent within a path-integral formulation. A general fluctuation-dissipation theorem is derived. The magnitude of the magnetic moment also fluctuates beyond the Gaussian approximation. We discuss how the approximate stochastic description of the thermal field follows from our result. As an example, we go beyond the linear-response method and show how the thermal fluctuations become anisotropy-dependent even in the uniaxial case.Comment: 22 page

Theory of finite temperature crossovers near quantum critical points close to, or above, their upper-critical dimension

A systematic method for the computation of finite temperature ($T$) crossover functions near quantum critical points close to, or above, their upper-critical dimension is devised. We describe the physics of the various regions in the $T$ and critical tuning parameter ($t$) plane. The quantum critical point is at $T=0$, $t=0$, and in many cases there is a line of finite temperature transitions at $T = T_c (t)$, $t < 0$ with $T_c (0) = 0$. For the relativistic, $n$-component $\phi^4$ continuum quantum field theory (which describes lattice quantum rotor ($n \geq 2$) and transverse field Ising ($n=1$) models) the upper critical dimension is $d=3$, and for $d<3$, $\epsilon=3-d$ is the control parameter over the entire phase diagram. In the region $|T - T_c (t)| \ll T_c (t)$, we obtain an $\epsilon$ expansion for coupling constants which then are input as arguments of known {\em classical, tricritical,} crossover functions. In the high $T$ region of the continuum theory, an expansion in integer powers of $\sqrt{\epsilon}$, modulo powers of $\ln \epsilon$, holds for all thermodynamic observables, static correlators, and dynamic properties at all Matsubara frequencies; for the imaginary part of correlators at real frequencies ($\omega$), the perturbative $\sqrt{\epsilon}$ expansion describes quantum relaxation at $\hbar \omega \sim k_B T$ or larger, but fails for $\hbar \omega \sim \sqrt{\epsilon} k_B T$ or smaller. An important principle, underlying the whole calculation, is the analyticity of all observables as functions of $t$ at $t=0$, for $T>0$; indeed, analytic continuation in $t$ is used to obtain results in a portion of the phase diagram. Our method also applies to a large class of other quantum critical points and their associated continuum quantum field theories.Comment: 36 pages, 4 eps figure

Exploring morphological correlations among H2CO, 12CO, MSX and continuum mappings

There are relatively few H2CO mappings of large-area giant molecular cloud (GMCs). H2CO absorption lines are good tracers for low-temperature molecular clouds towards star formation regions. Thus, the aim of the study was to identify H2CO distributions in ambient molecular clouds. We investigated morphologic relations among 6-cm continuum brightness temperature (CBT) data and H2CO (111-110; Nanshan 25-m radio telescope), 12CO (1--0; 1.2-m CfA telescope) and midcourse space experiment (MSX) data, and considered the impact of background components on foreground clouds. We report simultaneous 6-cm H2CO absorption lines and H110\alpha radio recombination line observations and give several large-area mappings at 4.8 GHz toward W49 (50'\times50'), W3 (70'\times90'), DR21/W75 (60'\times90') and NGC2024/NGC2023 (50'\times100') GMCs. By superimposing H2CO and 12CO contours onto the MSX color map, we can compare correlations. The resolution for H2CO, 12CO and MSX data was about 10', 8' and 18.3", respectively. Comparison of H2CO and 12CO contours, 8.28-\mu m MSX colorscale and CBT data revealed great morphological correlation in the large area, although there are some discrepancies between 12CO and H2CO peaks in small areas. The NGC2024/NGC2023 GMC is a large area of HII regions with a high CBT, but a H2CO cloud to the north is possible against the cosmic microwave background. A statistical diagram shows that 85.21% of H2CO absorption lines are distributed in the intensity range from -1.0 to 0 Jy and the \Delta V range from 1.206 to 5 km/s.Comment: 18 pages, 22 figures, 5 tables. Accepted to be published in Astrophysics and Space Scienc

Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

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