A.G., Tsukuba, 16 July New advances in numerical simulations of theta-vacuum systems V. Azcoiti, V. LalienaZaragoza U. G. Di CarloINFN-Gran Sasso A.G.L’Aquila U.- Gran Sasso hep-lat , , ,

A.G., Tsukuba, 16 July QFT + topological terms a special case of complex action the complex part of the action has a simple form: SU(N) with theta-term CP N-1 models Spin systems coupled to imaginary magnetic field.....

A.G., Tsukuba, 16 July density of topological charge P.d.F. of the order parameter PRL89 (2002) , hep-lat/ from real action simulations at use saddle point approx. get f(x) get use multiprecision code to compute use multiprecision code to compute

A.G., Tsukuba, 16 July the method has been tested in several cases: 2D compact U(1) with theta-term 1D AF Ising model coupled to imaginary magnetic field 2D CP 3 there are two possible sources of systematic effects: saddle point approx. a fit of simulation data is needed to have an analytical expression for f(x) need for independent results

A.G., Tsukuba, 16 July z = 0 z = 1 from y(z<1) we get

A.G., Tsukuba, 16 July z y(z) 1 real actioncomplex action related to real action complex action

A.G., Tsukuba, 16 July to extract information on CP symmetry at define: is a “free” parameter and the effective exponent gives information on

A.G., Tsukuba, 16 July D Ising model (data) CP symmetric model forbidden region

A.G., Tsukuba, 16 July in many models turns out to have a very mild dependence on y extrapolate seems a reasonable possibility (assume no phase transitions at real except at most at ) the extrapolation is “easier” for asymptotically free models where from real action simulations we can measure up to very small values of y results have to be independent of possible systematic effects

A.G., Tsukuba, 16 July how to extract from simulations we need y(z) for z<1 use the variable and plot vs y this function is again a very smooth one but a small region near the origin can not be determined by direct measurement from available data + the fit of the effective exponent we can extract for any y from, using an iterative procedure, we can extract y(z) and. PLB563 (2003) 117, hep-lat/

A.G., Tsukuba, 16 July (simulation data) (from data fit)

A.G., Tsukuba, 16 July D Ising model: exact and simulation a model without SSB: results for the order parameter

A.G., Tsukuba, 16 July D CP 3 model

A.G., Tsukuba, 16 July D CP 9 asymptotically free instantons solutions -vacua well defined topological charge + good asymptotic scaling z n 10 components scalar field U(1) gauge field U P =e iFp plaquette

A.G., Tsukuba, 16 July D CP 9 model results using P.d.F and the extrapolation procedure

A.G., Tsukuba, 16 July perturbative scaling non perturbative scaling

A.G., Tsukuba, 16 July Conclusions we propose two different methods to simulate theta-vacuum models (tested on analitically solvable models); both use real action (imaginary theta) simulations as input; the two methods can be affected by (different) systematic effects but agree each other; CP 9 results scale well with perturbative calculation and indicate SSB of CP symmetry at