Ising model is a generalized mathematical model of feromagnetism in statistical physics. In this model particles having magnetic spin are put inside vertices of graph. In general case structure of graph can vary a lot, but in the usual case selection is limited to the lattices of different dimensions. Behavior of such system is observed at different temperature in the quest to find critical temperature at which phase shift occurs. If you want to familiarize yourself more with Ising model and its various interpretations, you should read [1, 2] works, because in this text we will only consider one possible, numerical, algorithm - heat bath algorithm.

Previously on Physics of Risk website we have presented Kirman's ant colony agent-based model [1], where each ant was represented as an agent. In this article we will move from the agent-based model framework to the stochastic differential equation framework. Thus showing that in case of simple agent-based models full transition to stochastic framework is possible. This transition is very important as stochastic framework is very popular and well developed in quantitative finance. The problem is that stochastic framework mainly gives only a macroscopic insight into the modeled system, while microscopic behavior currently is also of big interest.

Vygintas Gontis, Julius Ruseckas and Aleksejus Kononovicius (2010). A Non-Linear Double Stochastic Model of Return in Financial Markets, Stochastic Control, Chris Myers (Ed.), ISBN: 978-953-307-121-3, Sciyo, Available from: https://www.intechopen.com/books/3748 – the latest review of research, done in the recent years, by scientists from Institute of Theoretical Physics and Astronomy, Vilnius University.

Physical interest in social systems, economics, financial markets and other so-called complex systems is growing for at least the last few decades. We have taken up interest in the financial markets back in 2004. Since then we have participated in European COST project Physics of Risk, which helped us maintain our present course. Recently we were invited to share our results with scientific community through the book named Stochastic Control. In 2010 this book was published by open access publisher sciyo.com, who has made electronic version of this book freely available at https://www.intechopen.com.

Next we briefly discuss our research and the scientific context, thus if you want to familiarize yourself more with our research you should start by reading chapter 27 of aforementioned book.

We, participants of project Science of business and society (lt. Mokslas verslui ir visuomenei), are happy to present renewed website dedicated to Physics of Risk. One of the obvious updates is new theme, but the look of site is not the only thing which has changed - from now on Physics of Risk will also be available in English!

As website is now available in two languages all of the old models, which were created for project Science. Scientists. Society (lt. Mokslas. Mokslininkai. Visuomenė), are now queued for minor improvements and translation. All of the old models are available in the copy of the old Physics of Risk website (though content is available only in Lithuanian).

More about the project and the website of Physics of Risk »

Here you can read the full Memorandum of Understanding for the implementation of a European Concerted Research Action designated as COST Action MP0801: Physics of Competition and Conflicts. See Memorandum of the COST action MP0801 »