Quantifying the Genetic Basis of Complex Diseases
I'm not sure what you mean by &quot;complex&quot;, but many diseases are known to arise due to exposure to toxins or to an absence of essential nutrients in the environment.
Toxic metals:
A good example of this is exposure to some metals including arsenic, lead, and mercury.  See for example this information from the US NIH and the wikipedia article on metal toxicity.
In the case of arsenic, some of this poisoning is even &quot;natural&quot; — i.e. due to toxic levels of this metal in ground water that hasn't been contaminated by human activity.
Diseases that have been linked to such exposures include cancer, heart disease, diabetes, and anemia.1,2
Deficiencies:
Another class of diseases that are more-or-less purely environmental are those due to nutrient deficiencies — i.e. a diet lacking in minerals or vitamins.

References:

Byrns, M. C., &amp; Penning, T. M. (2011). Environmental toxicology: carcinogens and heavy metals. The pharmacological basis of therapeutics. McGraw Hill, New York, 1853-1878.
Tolins, M., Ruchirawat, M., &amp; Landrigan, P. (2014). The developmental neurotoxicity of arsenic: cognitive and behavioral consequences of early life exposure. Annals of global health, 80(4), 303-314.