Given a simple self-dual quantum Hamiltonian H =KB +rB, where K and are coupling constants, and the condition that [B,[B,[B,B]]]=~~ [B,B], then we construct an infinite set of conserved charges Q2n; [H,Qzn] =O. In simple models, like the twodimensional Ising or Baxter eight-vertex, these charges appear in the associated quantum theories and are equivalent to those which result from the transfer-matrix formulation and exact quantum integrability of the system. The power of our result is that it is an operator statement and does not refer to the number of dimensions or the nature of the space-time manifold: lattice, continuum, or loop space, It is suggested how the establishment of this link between duality and integrability could be used to exploit the Kramers-Wannier-type self-duality of the four-dimensional SU(N) gauge theory to find hidden symmetry.

We study the three dimensional fundamental-adjoint SU(2) lattice gauge theory at finite temperature by Monte Carlo simulations. We find that the finite temperature deconfinement phase transition line joins the first order bulk phase transition line at its endpoint. Moreover, across the bulk transition line, the Polyakov loop undergoes a discontinuous jump implying the existence of both confining and deconfining phases on its two sides. Implications for universality and the nature of the confining-deconfining transition are discussed.

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We find a transformation relating the one-dimensional XY spin chain and the onedimensional quantum Ising model in a transverse magnetic field. This allows us to derive an infinite set of local conserved charges for the Ising model, which are exhibited explicitly.Jodd IJXP:P:+~+JI~]

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