Continuum limit on a 2-dimensional random lattice

We investigate the continuum limit of the Ising model on a 2-dimensional random lattice using Monte Carlo and strong coupling techniques. No evidence is found for deviation from the behaviour of the standard Ising model on a regular lattice; we do not see the modified critical properties found in the bond-diluted Ising model. Our results suggest that the continuum limit is the usual non-interacting Majorana fermion theory.     

Continuum QCD2 from a fixed-point lattice action

Gauge invariant expectation values for lattice gauge theory with a general local action in two dimensions may be expressed as functions of the single plaquette averages. The value of these averages at the fixed point of the renormalization group can be determined exactly, and the corresponding lattice theory is shown to reproduce the continuum results. The limit N_e = ∞ is investigated in detail, and fixed point values for all the averages are explicitly determined. Wilson's action results agree only to first order in weak coupling.     

Continuum limit of QED2 on a lattice

A path integral is defined for the vacuum expectation values of Euclidean QED₂ on a periodic lattice. Wilson's expression is used for the coupling between fermion and gauge fields. The action for the gauge field by itself is assumed to be a quadratic in place of Wilson's periodic action. The integral over the fermion field is carried out explicitly to obtain a Matthews-Salam formula for vacuum expectation values. For a combination of gauge and fermion fields $\text{G}$ on a lattice with spacing proportional to N^?1, N?Z⁺, the Matthews-Salam formula for the vacuum expectation 〈G〉_N has the form ($\text{G}$)_N=∫d_nu;W_N($\text{G}$,f), where dμ is an N-independent measure on a random electromagnetic field ? and $\text{W}{}_{\mathrm{N}}\text{(G, ?)}$ is an N-dependent function of ? determined by $\text{G}$. For a class of $\text{G}$ we prove that as N → ∞, $\text{W}{}_{\mathrm{N}}\text{(C, ?)}$ has a limit $\text{W(G, ?)}$ except possibly for a set of ? of measure zero. In subsequent articles it will be shown that ∫d_nu;W_N($\text{G}$,f) exists and lim_N→∞∫d_nu;W_N($\text{G}$,f).     

Continuum limit of A Z2 lattice gauge theory

Phase diagrams of lattice gauge theories have in several cases lines of first-order transitions ending at points at which continuous (second-order) transitions take place. In the vicinity of this critical point, a continuum field theory may be defined. We have analyzed here a Z₂ gauge plus matter model (which has no formal continuum limit) and identified the critical point with a usual Ø⁴, globally Z₂ invariant, field theory. The analysis relies on a mean field functional formalism and on a loop-wise expansion around it, which is reviewed.     

Continuum limit of lattice models built on quantum groups

We study the continuum limit of certain 2D lattice models built on quantum groups. Under the assumption that they renormalize to a Coulomb gas, we determine the central charge and critical exponents.     

Hydrogen bonded rings,chains and lassos: the case of t-butyl alcohol clusters

Infrared OH stretching spectra of hydrogen bonded 2-methyl-propan-2-01 (t-butyl alcohol) clusters are investigated by ragout-jet FTIR spectroscopy. A spectral difference technique is used to discriminate approximately between neighbouring cluster sizes. Dimers, trimers and cyclic tetramers can be detected along with larger clusters, which exhibit a surprisingly structured vibrational fingerprint. Comparison is made to the spectra of related alcohols and to energetic and harmonic vibrational predictions from electronic structure calculations. The experimentally observed 32% increase in OH stretching wavenumber shift from methanol dimer to t-butyl alcohol dimer is reproduced at the HF/3-21G level (+ 33%). It is also qualitatively correct at the MP2/6-31 +G* level (+ l5%), whereas it has the wrong sign at the B3LYP/6-31+ G* level (5%) and is negligible at the HF/6-31+ G* level, disregarding anharmonic effects. The cyclic tetramer of t-butyl alcohol is found to be particularly stable due to a favourable updown alternation of the bulky t-butyl groups. Beyond the t-butyl alcohol tetramer, lasso structures are found to be energetically competitive with simple ring structures. A many-body decomposition shows that this is due to a reduced cooperativity in the sterically hindered pentamer ring. The resulting thermodynamic and kinetic relevance of cyclic tetramers is discussed.     

Continuum limit of a hierarchical SU(2) lattice gauge theory in 4 dimensions

We study nonperturbative renormalizability of ad=4 hierarchical SU(2) gauge model that realizes Migdal's recursion relation as an exact renormalization group transformation. A continuum limit of effective actions is shown to exist as the scaling limit, both for initial Wilson and heat kernel actions. These limit effective actions exhibit ultraviolet asymptotic freedom and provide a strictly positive string tension.     

Continuum limit and improved action in lattice theories: (I). Principles and φ4 theory

Corrections to continuum theory results stemming from finite lattice spacing can be diminished systematically by use of lattice actions that also include suitable irrelevant terms. We describe in detail the principles of such constructions for the example of the φ⁴ theory.     

A convergence theorem for lattice Feynman integrals with massless propagators

It is shown that for non-vanishing lattice spacing, conventional infrared power counting conditions are sufficient for convergence of lattice Feynman integrals with zero-mass propagators. If these conditions are supplemented by ultraviolet convergence conditions, the continuum limit of such a diagram exists and is universal.     

On a cluster expansion for lattice spin systems: A finite-size condition for the convergence

A study is made of the statistical mechanics of classical lattice spin systems with finite-range interactions in two dimensions. By means of a decimation procedure, a finite-size condition is given for the convergence of a cluster expansion that is believed to be useful for treating the range of temperature between the critical oneT _c and the estimated thresholdT ₀ of convergence of the usual high-temperature expansion.     

A new large N phase transition in YM2

Inspired by the interpretation of two-dimensional Yang–Mills theory on a cylinder as a random walk on the gauge group, we point out the existence of a large N transition which is the gauge theory analogue of the cutoff transition in random walks. The transition occurs in the strong coupling region, with the 't Hooft coupling scaling as $\alpha \log N$, at a critical value of α ($\alpha =4$ on the sphere). The two phases below and above the transition are studied in detail. The effective number of degrees of freedom and the free energy are found to be proportional to $N^{2-\frac{\alpha }{2}}$ below the transition and to vanish altogether above it. The expectation value of a Wilson loop is calculated to the leading order and found to coincide in both phases with the strong coupling value.     

Continuum Nonsimple Loops and 2D Critical Percolation

Substantial progress has been made in recent years on the 2D critical percolation scaling limit and its conformal invariance properties. In particular, chordal SLE ₆(the Stochastic Loewner Evolution with parameter κ=6) was, in the work of Schramm and of Smirnov, identified as the scaling limit of the critical percolation “exploration process.” In this paper we use that and other results to construct what we argue is the fullscaling limit of the collection of allclosed contours surrounding the critical percolation clusters on the 2D triangular lattice. This random process or gas of continuum nonsimple loops in Bbb R²is constructed inductively by repeated use of chordal SLE ₆. These loops do not cross but do touch each other—indeed, any two loops are connected by a finite “path” of touching loops.     

The superconducting Kondo lattice: CeCu2Si2

Studying electric, magnetic, and thermolectric properties of Ce_xLa_1–xCu₂Si₂ alloys we have determined the variation of two principal parameters-T _k andT _RKKY -with concentrationx in the range 0<x1. The magnetic phase diagram of Ce_xLa_1-xCu₂Si₂ alloys has been found to be similar to that proposed by Doniach for the one-dimensional Kondo-necklace model. The anomalous low temperature properties of nonmagnetic Kondon lattices, including heavy fermion superconductivity, are related to the formate of the narrow Abrikosov-Suhl resonance in the vicinity of the Fermi level in concentrated Kondo systems withT _K T _RKKY .     

Energy band structures of the chalcopyrite lattice semiconductors CuAlS2, CuAlSe2, CuInS2, and CuInSe2

The pseudopotential method is used to calculate the energy band structures of four -type semiconductors including the effect of the displacement of anions from face-centered sites in the sublattices. It was established that CuAlSe₂, CuInS₂, and CuInSe₂ are direct gap semiconductors and that CuAlS₂ has a pseudodirect energy gap. Experimental data derived from studies of the optical properties of these crystals in the U V region are also discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 7–12, June, 1976.     

Black-hole production at LHC: Special features,problems, and expectations

A brief survey of the present-day status of the problem of multidimensional-black-hole production at accelerators according to models featuring large extra dimensions is given. The respective production cross section and the Hawking temperature and decay rate are estimated versus model parameters. Possible flaws and assumptions whose accurate inclusion can reduce significantly the probability of blackhole production at accelerators in relation to earlier optimistic estimates are also discussed.