Environmentally Friendly Renormalization

We analyze the renormalization of systems whose effective degrees of freedom are described in terms of fluctuations which are ``environment'' dependent. Relevant environmental parameters considered are: temperature, system size, boundary conditions, and external fields. The points in the space of \lq\lq coupling constants'' at which such systems exhibit scale invariance coincide only with the fixed points of a global renormalization group which is necessarily environment dependent. Using such a renormalization group we give formal expressions to two loops for effective critical exponents for a generic crossover induced by a relevant mass scale $g$. These effective exponents are seen to obey scaling laws across the entire crossover, including hyperscaling, but in terms of an effective dimensionality, d\ef=4-\gl, which represents the effects of the leading irrelevant operator. We analyze the crossover of an $O(N)$ model on a $d$ dimensional layered geometry with periodic, antiperiodic and Dirichlet boundary conditions. Explicit results to two loops for effective exponents are obtained using a [2,1] Pad\'e resummed coupling, for: the ``Gaussian model'' ($N=-2$), spherical model ($N=\infty$), Ising Model ($N=1$), polymers ($N=0$), XY-model ($N=2$) and Heisenberg ($N=3$) models in four dimensions. We also give two loop Pad\'e resummed results for a three dimensional Ising ferromagnet in a transverse magnetic field and corresponding one loop results for the two dimensional model. One loop results are also presented for a three dimensional layered Ising model with Dirichlet and antiperiodic boundary conditions. Asymptotically the effective exponents are in excellent agreement with known results.Comment: 76 pages of Plain Tex, Postscript figures available upon request from [email protected], preprint numbers THU-93/14, DIAS-STP-93-1

Geometry the Renormalization Group and Gravity

We discuss the relationship between geometry, the renormalization group (RG) and gravity. We begin by reviewing our recent work on crossover problems in field theory. By crossover we mean the interpolation between different representations of the conformal group by the action of relevant operators. At the level of the RG this crossover is manifest in the flow between different fixed points induced by these operators. The description of such flows requires a RG which is capable of interpolating between qualitatively different degrees of freedom. Using the conceptual notion of course graining we construct some simple examples of such a group introducing the concept of a ``floating'' fixed point around which one constructs a perturbation theory. Our consideration of crossovers indicates that one should consider classes of field theories, described by a set of parameters, rather than focus on a particular one. The space of parameters has a natural metric structure. We examine the geometry of this space in some simple models and draw some analogies between this space, superspace and minisuperspace.Comment: 16 pages of LaTex, DIAS-STP-92-3

Why Two Renormalization Groups are Better than One

The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very difficult to calculate with an RG based on one flow parameter may be much more accessible using another; ii) using more than one RG requires less physical input in order to describe via RG methods the theory as a function of its parameters; iii) using more than one RG allows one to solve problems with more than one diverging length scale. The above points are illustrated concretely in the context of both particle physics and statistical physics using the techniques of environmentally friendly renormalization. Specifically, finite temperature $\lambda\phi^4$ theory, an Ising-type system in a film geometry, an Ising-type system in a transverse magnetic field, the QCD coupling constant at finite temperature and the crossover between bulk and surface critical behaviour in a semi-infinite geometry are considered.Comment: 17 pages LaTex; to be published in the Proceedings of RG '96, Dubn

Phosphorylation of Subunit Proteins of Intermediate Filaments from Chicken Muscle and Nonmuscle Cells

The phosphorylation of the subunit proteins of intermediate (10-nm) filaments has been investigated in chicken muscle and nonmuscle cells by using a two-dimensional gel electrophoresis system. Desmin, the 50,000-dalton subunit protein of the intermediate filaments of muscle, had previously been shown to exist as two major isoelectric variants--alpha and ß --in smooth, skeletal, and cardiac chicken muscle. Incubation of skeletal and smooth muscle tissue with 32PO4{}3- reveals that the acidic variant, alpha -desmin, and three other desmin variants are phosphorylated in vivo and in vitro. Under the same conditions, minor components of alpha - and ß -tropomyosin from skeletal muscle, but not smooth muscle, are also phosphorylated. Both the phosphorylated desmin variants and the nonphosphorylated ß -desmin variant remain insoluble under conditions that solubilize actin and myosin filaments, but leave Z-discs and intermediate filaments insoluble. Primary cultures of embryonic chicken muscle labeled with 32PO4{}3- possess, in addition to the desmin variants described above, a major nonphosphorylated and multiple phosphorylated variants of the 52,000-dalton, fibroblast-type intermediate filament protein (IFP). Filamentous cytoskeletons, prepared from primary myogenic cultures by Triton X-100 extraction, contain actin and all of the phosphorylated and nonphosphorylated variants of both desmin and the IFP. Similarly, these proteins are the major components of the caps of aggregated 10-nm filaments isolated from the same cell cultures previously exposed to Colcemid. These results demonstrate that a nonphosphorylated and several phosphorylated variants of desmin and IFP are present in assembled structures in muscle and nonmuscle cells

An investigation of the relationship between rumination styles, hope, and suicide ideation through the lens of the integrated motivational-volitional model of suicidal behavior

To investigate the roles specific ruminative styles (brooding and reflection) and hope play in the Integrated Motivational-Volitional (IMV) model of suicidal behavior. Participants were students from a large U.S. state university who were selectively sampled for the experience of recent suicide ideation. Results of a bootstrapped moderated mediation model indicated that defeat had a direct effect on suicide ideation but not an indirect effect on suicide ideation through entrapment. Brooding, but not reflection, strengthened the relationship between defeat and entrapment. Hope weakened the relationship between entrapment and suicide ideation. Implications for the assessment and treatment of suicide risk and future research directions are discussed

Critical Temperature and Amplitude Ratios from a Finite-Temperature Renormalization Group

We study \l\f^4 theory using an environmentally friendly finite-temperature renormalization group. We derive flow equations, using a fiducial temperature as flow parameter, develop them perturbatively in an expansion free from ultraviolet and infrared divergences, then integrate them numerically from zero to temperatures above the critical temperature. The critical temperature, at which the mass vanishes, is obtained by integrating the flow equations and is determined as a function of the zero-temperature mass and coupling. We calculate the field expectation value and minimum of the effective potential as functions of temperature and derive some universal amplitude ratios which connect the broken and symmetric phases of the theory. The latter are found to be in good agreement with those of the three-dimensional Ising model obtained from high- and low-temperature series expansions.Comment: 14 pages of LaTeX. Postscript figures available upon request form [email protected]

Research Methodology. ESRI Memorandum Series No. 98 1974

In his talk last week Dr. Kennedy outlined how he organized research and in the course of his address stated that he was concentrating on the nuts and bolts of the operation rather than on the more exciting intellectual matters of objectivity, causality, creativity, inspiration, induction and deduction. It is my function to talk about the latter topics but in the time at my disposal I can cover very little of this ground. I propose therefore to confine my remarks to a discussion of research methodology or to what is known as "the theory of inquiry". As an introduction to this subject I will speak briefly about deduction and induction and conclude by giving an example of the application of these ideas in a practical situation