Isospin susceptibility in the O(nn) sigma-model in the delta-regime

We compute the isospin susceptibility in an effective O($n$) scalar field theory (in $d=4$ dimensions), to third order in chiral perturbation theory ($\chi$PT) in the delta--regime using the quantum mechanical rotator picture. This is done in the presence of an additional coupling, involving a parameter $\eta$, describing the effect of a small explicit symmetry breaking term (quark mass). For the chiral limit $\eta=0$ we demonstrate consistency with our previous $\chi$PT computations of the finite-volume mass gap and isospin susceptibility. For the massive case by computing the leading mass effect in the susceptibility using $\chi$PT with dimensional regularization, we determine the $\chi$PT expansion for $\eta$ to third order. The behavior of the shape coefficients for long tube geometry obtained here might be of broader interest. The susceptibility calculated from the rotator approximation differs from the $\chi$PT result in terms vanishing like $1/\ell$ for $\ell=L_t/L_s\to\infty$. We show that this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant.Comment: 34 page

Locality and exponential error reduction in numerical lattice gauge theory

In non-abelian gauge theories without matter fields, expectation values of large Wilson loops and loop correlation functions are difficult to compute through numerical simulation, because the signal-to-noise ratio is very rapidly decaying for increasing loop sizes. Using a multilevel scheme that exploits the locality of the theory, we show that the statistical errors in such calculations can be exponentially reduced. We explicitly demonstrate this in the SU(3) theory, for the case of the Polyakov loop correlation function, where the efficiency of the simulation is improved by many orders of magnitude when the area bounded by the loops exceeds 1 fm^2.Comment: Plain TeX source, 18 pages, figures include

One-loop renormalization factors and mixing coeffecients of bilinear quark operators for improved gluon and quark actions

We calculate one-loop renormalization factors and mixing coefficients of bilinear quark operators for a class of gluon actions with six-link loops and O(a)-improved quark action. The calculation is carried out by evaluating on-shell Green's functions of quarks and gluons in the standard perturbation theory. We find a general trend that finite parts of one-loop coefficients are reduced approximately by a factor two for the renormalization-group improved gluon actions compared with the case of the standard plaquette gluon action.Comment: LATTICE98(improvement), 3 page

Square Symanzik action to one-loop order

We present the one-loop coefficients for an alternative Symanzik improved lattice action with gauge groups SU(2) or SU(3).Comment: 3 pages, latex, 1 table, no figure

Physical and Monetary Input-Output Analysis: What Makes the Difference?

A recent paper in which embodied land appropriation of exports was calculated using a physical input-output model (Ecological Economics 44 (2003) 137-151) initiated a discussion in this journal concerning the conceptual differences between input-output models using a coefficient matrix based on physical input-output tables (PIOTs) in a single unit of mass and input-output models using a coefficient matrix based on monetary input-output tables (MIOTs) extended by a coefficient vector of physical factor inputs per unit of output. In this contribution we argue that the conceptual core of the discrepancies found when comparing outcomes obtained using physical vs. monetary input-output models lies in the assumption of prices and not in the treatment of waste as has been claimed (Ecological Economics 48 (2004) 9-17). We first show that a basic static input-output model with the coefficient matrix derived from a monetary input-output table is equivalent to one where the coefficient matrix is derived from an input-output table in physical units provided that the assumption of unique sectoral prices is satisfied. We then illustrate that the physical input-output table that was used in the original publication does not satisfy the assumption of homogenous sectoral prices, even after the inconsistent treatment of waste in the PIOT is corrected. We show that substantially different results from the physical and the monetary models in fact remain. Finally, we identify and discuss possible reasons for the observed differences in sectoral prices and draw conclusions for the future development of applied physical input-output analysis.