Give them plenty of water and feed regularly. That's really all there is too it!

First, what's wrong with one inch wide? If your carrots have no root at all going down off that 2 inch section, I'd suspect that seed wasn't Scarlet Nantes.

Are they fully mature? When carrots mature, the stems thicken up and flatten down to the ground. I don't harvest mine until I see that happen.

Thank you for your responses!

tommyr: I believe the bed has stayed fairly moist. What fertilizer do you use for your carrots? How long does it typically take to harvest them?

jonfrum: I have no issue with the width, it's more the length. They do have some long roots on them when I pick them. It is Scarlett Nantes (I still have the seed package). The package says they should be ready to harvest in 70 days, and that the roots are 6-7" ... which is what has me worried since they've been in the ground for twice that amount of time now (almost 140 days). The stems are still upright for the most part; some of the outer stems have laid down though.

Use regular Miracle grow or a 10-10-10 or 20-20-20. Follow label directions as always. I go by the seed packet instructions. Also, around the time they are supposed to be ready I carefully check one to see if they are ready.

are they planted near tomatoes? carrots near tomatoes will be somewhat stunted. I have read and observed this - the carrot looks good on top, but when you pull it out it is normal size width wise - yet only 2-3 inches long.

It sounds to me like you could have another variety, like Short and Sweet. It's a new raised bed, so your soil wasn't compacted. A lack of fertilizer wouldn't produce that exact limit on growth - the roots would be scrawny as well. I'd definitely try different seen for the fall crop.

i have to concur with tommyr- it does sound like a nutrient defieincy. use a 10-10-10 or 13-13-13 fert 1 cup for every 10 feet of row.
a picture of the carrots would be useful also in determining what the cause is.

Are they planted far enough apart?

Here's a pic -- I put the teaspoon next to the carrot for perspective.

akaRach: I believe so, and I thinned them too after they sprouted --about 3 " apart. And the rows are maybe 10" apart.

t-bird: No they're not with tomatoes, though I do have strawberries in the same raised bed.

my opinion this is showing poor growing conditions, overcrowding and not enough nutrients. tall tops on the carrots. looks like it was reaching for light. the carrot is also light in color due to poor nutrients.

There definitely is something wrong. You would think the tap root would be longer. Are you watering too much? I wonder if watering too much would basically keep the carrot a certain length, because it doesn't need to dig down further to reach more nutrients.

Here is a Nantes carrot I pulled yesterday.
{{gwi:81622}}

Another possibility:
Could they be getting too much shade after other things have leaved out? I have had carrots stall out like that when the trees over one of my beds start to really block the light out in late June or so. If the carrots haven't matured by then, I don't get much. The plant will continue to grow, but just very slowly, and many of the carrots turn out woody and dry. However, once I had this happen with 4 different varieties I was trying out. Scarlet Nantes was the only one that produced edible carrots. But it was 2 months later than I normally would have harvested.