The multi-GPU open-source package QCDGPU for lattice Monte Carlo simulations of pure SU(N) gluodynamics in external magnetic field at finite temperature and O(N) model is developed. The code is implemented in OpenCL, tested on AMD and NVIDIA GPUs, AMD and Intel CPUs and may run on other OpenCL-compatible devices. The package contains minimal external library dependencies and is OS platform-independent. It is optimized for heterogeneous computing due to the possibility of dividing the lattice into non-equivalent parts to hide the difference in performances of the devices used. QCDGPU has client-server part for distributed simulations. The package is designed to produce lattice gauge configurations as well as to analyze previously generated ones. QCDGPU may be executed in fault-tolerant mode. Monte Carlo procedure core is based on PRNGCL library for pseudo-random numbers generation on OpenCL-compatible devices, which contains several most popular pseudo-random number generators.

The spontaneous generation of homogeneous chromomagnetic fields in the lattice SU(3) gluodynamics is investigated in the deconfinement phase of the model. A new approach based on direct measurements of the field strength on a lattice is developed. Vacuum magnetization is established by its influence on the probability density function of the simulated field strength. It is found that both the chromomagnetic fields corresponding to the diagonal SU(3) generators are simultaneously condensated and appear to be spatially co-directed. No vacuum magnetization is detected for the other SU(3) components. The temperature dependence of the spontaneously generated fields in physical units is fitted in the temperature interval 200 MeV -200 GeV as the usual power law with the anomalous dimension.

In this proceeding we present our first results of the study of the QCD Equation of State at nonzero baryon density and in external magnetic field. We focused on the first three non-vanishing expansion coefficients of pressure in chemical potential and their dependence on magnetic field. The study is carried out within lattice simulations with 𝑁 𝑓 = 2 + 1 dynamical quarks with physical quark masses. To overcome the sign problem, the simulations are carried out at imaginary baryon chemical potential. Our results suggest that external magnetic field considerably enhances the expansion coefficients and modifies their dependence on temperature.

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