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seeds Help - deformed seedlings

Hi - I have attached a couple of photos of these seedlings that I have raised from seed.  There has been lots of leaf deformation and I am at a loss as to what could be the problem.  Here are the background facts:
  • Grown from seeds using a combination of paper towel method and direct in rock wool
  • All were purchased from the hippy seed company
  • Once sprouted transferred to a soil made of equal parts peat moss, compost and vermiculite
  • upon second set of leaves, diluted worm juice used to water
  • Look good with initial set of leaves
  • Grown under LED lighting with a heat mat underneath
Lots of the seedlings are exhibiting the same problems with some severely deformed.
Any help / thoughts appreciated.

Those plants look very tall , even sideways, it might be to hot with the lights and heat mat .
A heat mat will also dry your soil within hours.
My opinion; heat and drought.
Yeah, the heat mat really isn't necessary after the seeds have germinated. You should also rethink using vermiculite. It's normally used in potting mixes for water-loving plants, which peppers aren't. Perlite might me a better option.
Contrary to what karoo said; how often and how much are you watering the plants? The quick evaporation with the heat mat might add up to the age-old beginner's mistake of watering too much. 
Edit: Also, what kind of LED lighting are you using?