  From the Bretton Woods agreement in 1944 till the present day, the US dollar
has been the dominant currency in the world trade. However, the rise of the
Chinese economy led recently to the emergence of trade transactions in Chinese
yuan. Here, we analyze mathematically how the structure of the international
trade flows would favor a country to trade whether in US dollar or in Chinese
yuan. The computation of the trade currency preference is based on the world
trade network built from the 2010-2020 UN Comtrade data. The preference of a
country to trade in US dollar or Chinese yuan is determined by two
multiplicative factors: the relative weight of trade volume exchanged by the
country with its direct trade partners, and the relative weight of its trade
partners in the global international trade. The performed analysis, based on
Ising spin interactions on the world trade network, shows that, from 2010 to
present, a transition took place, and the majority of the world countries would
have now a preference to trade in Chinese yuan if one only consider the world
trade network structure.
