Critical Behaviour of the 3d Gross-Neveu and Higgs-Yukawa Models

We measure the critical exponents of the three dimensional Gross-Neveu model with two four-component fermions. The exponents are inferred from the scaling behaviour of observables on different lattice sizes. We also calculate the exponents, through a second order epsilon-expansion around 4d, for the three dimensional Higgs-Yukawa model, which is expected to be in the same universality class and we find that the exponents agree. We conclude that the equivalence of the two models remains valid in 3d at fixed small N_f values.Comment: 14 Latex pages 8 PSfigures included at the end,BI-TP-93/31,AZPH-TH/93-19,SPhT 93/0

Three dimensional finite temperature SU(3) gauge theory in the confined region and the string picture

We determine the correlation between Polyakov loops in three dimensional SU(3) gauge theory in the confined region at finite temperature. For this purpose we perform lattice calculations for the number of steps in the temperature direction equal to six. This is expected to be in the scaling region of the lattice theory. We compare the results to the bosonic string model. The agreement is very good for temperatures T<0.7T_c, where T_c is the critical temperature. In the region 0.7T_c<T<T_c we enter the critical region, where the critical properties of the correlations are fixed by universality to be those of the two dimensional three state Potts model. Nevertheless, by calculating the critical lattice coupling, we show that the ratio of the critical temperature to the square root of the zero temperature string tension, where the latter is taken from the literature, remains very near to the string model prediction.Comment: 11 pages, 1 figure, 1 tabl

Random matrix model for QCD_3 staggered fermions

We show that the lowest part of the eigenvalue density of the staggered fermion operator in lattice QCD_3 at small lattice coupling constant beta has exactly the same shape as in QCD_4. This observation is quite surprising, since universal properties of the QCD_3 Dirac operator are expected to be described by a non-chiral matrix model. We show that this effect is related to the specific nature of the staggered fermion discretization and that the eigenvalue density evolves towards the non-chiral random matrix prediction when beta is increased and the continuum limit is approached. We propose a two-matrix model with one free parameter which interpolates between the two limits and very well mimics the pattern of evolution with beta of the eigenvalue density of the staggered fermion operator in QCD_3.Comment: 8 pages 4 figure

Albert algebras over Z and other rings

Albert algebras, a specific kind of Jordan algebra, are naturally distinguished objects among commutative non-associative algebras and also arise naturally in the context of simple affine group schemes of type $F_4$, $E_6$, or $E_7$. We study these objects over an arbitrary base ring $R$, with particular attention to the case of the integers. We prove in this generality results previously in the literature in the special case where $R$ is a field of characteristic different from 2 and 3.Comment: v2: section 12 on number of generators is new, Theorem 13.5 now holds for semi-local rings (and even a somewhat wider class

Voltage-Controlled Superconducting Quantum Bus

We demonstrate the ability of an epitaxial semiconductor-superconductor nanowire to serve as a field-effect switch to tune a superconducting cavity. Two superconducting gatemon qubits are coupled to the cavity, which acts as a quantum bus. Using a gate voltage to control the superconducting switch yields up to a factor of 8 change in qubit-qubit coupling between the on and off states without detrimental effect on qubit coherence. High-bandwidth operation of the coupling switch on nanosecond timescales degrades qubit coherence