  This paper provides a general method to directly translate a classical
economic framework with a large number of agents into a field-formalism model.
This type of formalism allows the analytical treatment of economic models with
an arbitrary number of agents, while preserving the system's interactions and
microeconomic features of the individual level.We apply this methodology to
model the interactions between financial markets and the real economy,
described in a classical framework of a large number of heterogeneous agents,
investors and firms. Firms are spread among sectors but may shift between
sectors to improve their returns. They compete by producing differentiated
goods and reward their investors by paying dividends and through their stocks'
valuation. Investors invest in firms and move along sectors based on firms'
expected long-run returns.The field-formalism model derived from this framework
allows for collective states to emerge. We show that the number of firms in
each sector depends on the aggregate financial capital invested in the sector
and its firms' expected long-term returns. Capital accumulation in each sector
depends both on short-term returns and expected long-term returns relative to
neighbouring sectors.For each sector, three patterns of accumulation emerge. In
the first pattern, the dividend component of short-term returns is determinant
for sectors with small number of firms and low capital. In the second pattern,
both short and long-term returns in the sector drive intermediate-to-high
capital. In the third pattern, higher expectations of long-term returns drive
massive inputs of capital.Instability in capital accumulation may arise among
and within sectors. We therefore widen our approach and study the dynamics of
the collective configurations, in particular interactions between average
capital and expected long-term returns, and show that overall stability
crucially depends on the expectations' formation process.Expectations that are
highly reactive to capital variations stabilize high capital configurations,
and drive low-to-moderate capital sectors towards zero or a higher level of
capital, depending on their initial capital. Inversely, low-to moderate capital
configurations are stabilized by expectations moderately reactive to capital
variations, and drive high capital sectors towards more moderate level of
capital equilibria.Eventually, the combination of expectations both highly
sensitive to exogenous conditions and highly reactive to variations in capital
imply that large fluctuations of capital in the system, at the possible expense
of the real economy.
